Theorem. (
t34_domain_1)
∀esk7_5 : set → set → set → set → set → set, ∀a_4_4_domain_1 : set → set → set → set → set, ∀a_3_6_domain_1 : set → set → set → set, ∀esk5_4 : set → set → set → set → set, ∀k5_subset_1 : set → set → set → set, ∀v1_relat_1 : set → prop, ∀v1_subset_1 : set → set → prop, ∀r1_tarski : set → set → prop, ∀esk10_1 : set → set, ∀v2_relat_1 : set → prop, ∀k1_xboole_0 : set, ∀esk15_1 : set → set, ∀esk14_0 : set, ∀esk4_1 : set → set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk12_0 : set, ∀esk13_1 : set → set, ∀esk9_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀v3_relat_1 : set → prop, ∀esk16_1 : set → set, ∀esk18_2 : set → set → set, ∀k4_xboole_0 : set → set → set, ∀k2_xboole_0 : set → set → set, ∀esk6_4 : set → set → set → set → set, ∀a_3_8_domain_1 : set → set → set → set, ∀esk17_4 : set → set → set → set → set, ∀a_4_6_domain_1 : set → set → set → set → set, ∀esk8_5 : set → set → set → set → set → set, ∀r2_hidden : set → set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, (∀X2 X3 X1 X4 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_6_domain_1 X2 X3 X4 X5) → r2_hidden (esk8_5 X1 X2 X3 X4 X5) X4 → r2_hidden (esk8_5 X1 X2 X3 X4 X5) X3 → False) → (∀X2 X3 X1 X4 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_4_domain_1 X2 X3 X4 X5) → r2_hidden (esk7_5 X1 X2 X3 X4 X5) X4 → r2_hidden (esk7_5 X1 X2 X3 X4 X5) X3 → False) → (∀X2 X3 X1 X4 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → (r2_hidden (esk8_5 X1 X2 X3 X4 X5) X4 → False) → (r2_hidden (esk8_5 X1 X2 X3 X4 X5) X3 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_6_domain_1 X2 X3 X4 X5) → False) → (∀X2 X3 X1 X4 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → (r2_hidden (esk7_5 X1 X2 X3 X4 X5) X4 → False) → (r2_hidden (esk7_5 X1 X2 X3 X4 X5) X3 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_4_domain_1 X2 X3 X4 X5) → False) → (∀X2 X3 X1 X4 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 (esk8_5 X1 X2 X3 X4 X5) X5 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_6_domain_1 X2 X3 X4 X5) → False) → (∀X2 X3 X1 X4 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 (esk7_5 X1 X2 X3 X4 X5) X5 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_4_domain_1 X2 X3 X4 X5) → False) → (∀X1 X2 X3 X4, ((a_4_4_domain_1 X1 X2 X3 X4) = (a_4_6_domain_1 X1 X2 X3 X4) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X1 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → r2_hidden (esk17_4 X1 X2 X3 X4) X3 → r2_hidden (esk17_4 X1 X2 X3 X4) X2 → False) → (∀X2 X3 X1 X4 X5, ((esk8_5 X1 X2 X3 X4 X5) = X1 → False) → (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_6_domain_1 X2 X3 X4 X5) → False) → (∀X2 X3 X1 X4 X5, ((esk7_5 X1 X2 X3 X4 X5) = X1 → False) → (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_4_4_domain_1 X2 X3 X4 X5) → False) → (∀X1 X2 X3 X4, ((a_4_4_domain_1 X1 X2 X3 X4) = (a_4_6_domain_1 X1 X2 X3 X4) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X1 → False) → (r2_hidden (esk17_4 X1 X2 X3 X4) X2 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → r2_hidden (esk17_4 X1 X2 X3 X4) X3 → False) → (∀X1 X2 X3 X4, ((a_4_4_domain_1 X1 X2 X3 X4) = (a_4_6_domain_1 X1 X2 X3 X4) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X1 → False) → (r2_hidden (esk17_4 X1 X2 X3 X4) X3 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → r2_hidden (esk17_4 X1 X2 X3 X4) X2 → False) → (∀X4 X1 X3 X2, (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_6_domain_1 X2 X3 X4) → r2_hidden (esk5_4 X1 X2 X3 X4) X4 → r2_hidden (esk5_4 X1 X2 X3 X4) X3 → False) → (∀X4 X1 X3 X2, (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_8_domain_1 X2 X3 X4) → r2_hidden (esk6_4 X1 X2 X3 X4) X4 → r2_hidden (esk6_4 X1 X2 X3 X4) X3 → False) → (∀X1 X3 X2 X4, ((a_4_4_domain_1 X1 X2 X3 X4) = (a_4_6_domain_1 X1 X2 X3 X4) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X1 → False) → (r2_hidden (esk17_4 X1 X2 X3 X4) X3 → False) → (r2_hidden (esk17_4 X1 X2 X3 X4) X2 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X4 X1 X3 X2, (v1_xboole_0 X2 → False) → (r2_hidden (esk6_4 X1 X2 X3 X4) X4 → False) → (r2_hidden (esk6_4 X1 X2 X3 X4) X3 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_8_domain_1 X2 X3 X4) → False) → (∀X4 X1 X3 X2, (v1_xboole_0 X2 → False) → (r2_hidden (esk5_4 X1 X2 X3 X4) X4 → False) → (r2_hidden (esk5_4 X1 X2 X3 X4) X3 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_6_domain_1 X2 X3 X4) → False) → (∀X1 X3 X2 X4, ((a_4_4_domain_1 X1 X2 X3 X4) = (a_4_6_domain_1 X1 X2 X3 X4) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (esk17_4 X1 X2 X3 X4) X4 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X4 X1 X3 X2, (v1_xboole_0 X2 → False) → (m1_subset_1 (esk6_4 X1 X2 X3 X4) X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_8_domain_1 X2 X3 X4) → False) → (∀X4 X1 X3 X2, (v1_xboole_0 X2 → False) → (m1_subset_1 (esk5_4 X1 X2 X3 X4) X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_6_domain_1 X2 X3 X4) → False) → (∀X4 X5 X3 X1 X2 X6, (v1_xboole_0 X6 → False) → (v1_xboole_0 X4 → False) → (r2_hidden X1 X2 → False) → (r2_hidden X5 (a_4_4_domain_1 X6 X2 X3 X4) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X3 → m1_subset_1 X3 (k1_zfmisc_1 X6) → m1_subset_1 X2 (k1_zfmisc_1 X6) → False) → (∀X4 X5 X2 X1 X3 X6, (v1_xboole_0 X6 → False) → (v1_xboole_0 X4 → False) → (r2_hidden X1 X3 → False) → (r2_hidden X5 (a_4_6_domain_1 X6 X2 X3 X4) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X6) → m1_subset_1 X2 (k1_zfmisc_1 X6) → False) → (∀X4 X5 X2 X1 X3 X6, (v1_xboole_0 X6 → False) → (v1_xboole_0 X4 → False) → (r2_hidden X1 X3 → False) → (r2_hidden X5 (a_4_6_domain_1 X6 X3 X2 X4) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X6) → m1_subset_1 X2 (k1_zfmisc_1 X6) → False) → (∀X4 X5 X2 X1 X3 X6, (v1_xboole_0 X6 → False) → (v1_xboole_0 X4 → False) → (r2_hidden X1 X3 → False) → (r2_hidden X5 (a_4_4_domain_1 X6 X2 X3 X4) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X6) → m1_subset_1 X2 (k1_zfmisc_1 X6) → False) → (∀X4 X1 X3 X2, ((esk6_4 X1 X2 X3 X4) = X1 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_8_domain_1 X2 X3 X4) → False) → (∀X4 X1 X3 X2, ((esk5_4 X1 X2 X3 X4) = X1 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_6_domain_1 X2 X3 X4) → False) → (∀X2 X1 X3 X5 X4, (v1_xboole_0 X4 → False) → (r2_hidden X1 X2 → False) → (r2_hidden X5 (a_3_6_domain_1 X4 X2 X3) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X3 → m1_subset_1 X3 (k1_zfmisc_1 X4) → m1_subset_1 X2 (k1_zfmisc_1 X4) → False) → (∀X3 X1 X2 X5 X4, (v1_xboole_0 X4 → False) → (r2_hidden X1 X3 → False) → (r2_hidden X5 (a_3_6_domain_1 X4 X2 X3) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X4) → m1_subset_1 X2 (k1_zfmisc_1 X4) → False) → (∀X3 X1 X2 X5 X4, (v1_xboole_0 X4 → False) → (r2_hidden X1 X3 → False) → (r2_hidden X5 (a_3_8_domain_1 X4 X2 X3) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X4) → m1_subset_1 X2 (k1_zfmisc_1 X4) → False) → (∀X3 X1 X2 X5 X4, (v1_xboole_0 X4 → False) → (r2_hidden X1 X3 → False) → (r2_hidden X5 (a_3_8_domain_1 X4 X3 X2) → False) → X1 = X5 → m1_subset_1 X1 X4 → r2_hidden X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X4) → m1_subset_1 X2 (k1_zfmisc_1 X4) → False) → (∀X3 X2 X1, (m1_subset_1 (k5_subset_1 X2 X1 X3) (k1_zfmisc_1 X2) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k5_subset_1 X2 X1 X3) = (k2_xboole_0 (k4_xboole_0 X1 X3) (k4_xboole_0 X3 X1)) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X3 X1, ((a_3_6_domain_1 X1 X2 X3) = (k5_subset_1 X1 X2 X3) → False) → (v1_xboole_0 X1 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X3 X2 X1, ((k5_subset_1 X2 X1 X3) = (k5_subset_1 X2 X3 X1) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (v1_relat_1 (k2_xboole_0 (k4_xboole_0 X1 X2) (k4_xboole_0 X2 X1)) → False) → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk18_2 X3 X2) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (r2_hidden (esk18_2 X1 X2) X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1, v1_xboole_0 X1 → v1_subset_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → 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) → (∀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, (v1_relat_1 (k2_xboole_0 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1 X2, (v1_relat_1 X2 → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_relat_1 (k4_xboole_0 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk10_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk16_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk10_1 X1) → False) → (∀X1, (v2_relat_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_relat_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((a_3_8_domain_1 esk1_0 esk2_0 esk3_0) = (k5_subset_1 esk1_0 esk2_0 esk3_0) → False) → (∀X1, v1_subset_1 (esk15_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk9_0 → False) → (v1_xboole_0 esk1_0 → False) → (∀X2 X1, ((k2_xboole_0 (k4_xboole_0 X1 X2) (k4_xboole_0 X2 X1)) = (k2_xboole_0 (k4_xboole_0 X2 X1) (k4_xboole_0 X1 X2)) → False) → False) → (∀X1, ((k2_xboole_0 (k4_xboole_0 X1 k1_xboole_0) (k4_xboole_0 k1_xboole_0 X1)) = X1 → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk13_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk4_1 X1) X1 → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 esk1_0) → False) → False) → ((m1_subset_1 esk2_0 (k1_zfmisc_1 esk1_0) → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k4_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k4_xboole_0 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → (∀X1, (v1_xboole_0 (esk13_1 X1) → False) → False) → ((v2_relat_1 esk12_0 → False) → False) → ((v1_relat_1 esk12_0 → False) → False) → ((v1_relat_1 esk9_0 → False) → False) → ((v1_xboole_0 esk11_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