Theorem. (
t4_xregular)
∀k3_tarski : set → set, ∀esk7_2 : set → set → set, ∀esk11_1 : set → set, ∀esk8_2 : set → set → set, ∀esk15_2 : set → set → set, ∀esk4_1 : set → set, ∀esk3_1 : set → set, ∀esk17_1 : set → set, ∀esk10_0 : set, ∀esk9_0 : set, ∀k1_xboole_0 : set, ∀esk2_1 : set → set, ∀esk1_0 : set, ∀esk18_2 : set → set → set, ∀esk13_2 : set → set → set, ∀esk12_2 : set → set → set, ∀esk14_1 : set → set, ∀r1_xboole_0 : set → set → prop, ∀esk16_1 : set → set, ∀v1_xboole_0 : set → prop, ∀esk6_3 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀esk5_3 : set → set → set → set, ∀k2_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk5_3 X1 X2 X3) X3 → r2_hidden (esk5_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk5_3 X1 X2 X3) X3 → r2_hidden (esk5_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (r2_hidden (esk5_3 X1 X2 X3) X2 → False) → (r2_hidden (esk5_3 X1 X2 X3) X1 → False) → False) → (∀X3 X2 X1, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk7_2 X1 X2) X3 → r2_hidden (esk7_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk6_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk6_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r1_xboole_0 X1 X2 → False) → (r2_hidden X1 (esk16_1 X2) → False) → r2_hidden X1 (k3_tarski (k3_tarski (k3_tarski X2))) → False) → (∀X3 X4 X1 X2, (v1_xboole_0 X2 → False) → (r1_xboole_0 X3 X2 → False) → (r2_hidden X1 (esk11_1 X2) → False) → r2_hidden X4 X1 → r2_hidden X3 X4 → r2_hidden X1 (k3_tarski X2) → False) → (∀X3 X1 X2, (v1_xboole_0 X2 → False) → (r1_xboole_0 X3 X2 → False) → (r2_hidden X1 (esk14_1 X2) → False) → r2_hidden X3 X1 → r2_hidden X1 (k3_tarski (k3_tarski X2)) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → (r2_hidden (esk7_2 X1 X2) (esk8_2 X1 X2) → False) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (r2_hidden (esk12_2 X1 X2) (esk13_2 X1 X2) → False) → r2_hidden X2 (esk11_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → r2_hidden X2 (esk14_1 X1) → r1_xboole_0 (esk15_2 X1 X2) X1 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → r2_hidden X2 (esk11_1 X1) → r1_xboole_0 (esk12_2 X1 X2) X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 (k3_tarski (k3_tarski (k3_tarski X2))) → False) → r2_hidden X1 (esk16_1 X2) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → (r2_hidden (esk8_2 X1 X2) X1 → False) → False) → (∀X3 X2 X1, (r1_xboole_0 X1 (k2_xboole_0 X2 X3) → False) → r1_xboole_0 X1 X3 → r1_xboole_0 X1 X2 → False) → (∀X3 X1 X2, (r1_xboole_0 X1 X2 → False) → r1_xboole_0 X1 (k2_xboole_0 X2 X3) → False) → (∀X3 X1 X2, (r1_xboole_0 X1 X2 → False) → r1_xboole_0 X1 (k2_xboole_0 X3 X2) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (r2_hidden (esk15_2 X1 X2) X2 → False) → r2_hidden X2 (esk14_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (r2_hidden (esk13_2 X1 X2) X2 → False) → r2_hidden X2 (esk11_1 X1) → 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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 (k3_tarski (k3_tarski X2)) → False) → r2_hidden X1 (esk14_1 X2) → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_tarski X3) → r2_hidden X2 X3 → r2_hidden X1 X2 → False) → (∀X2 X1 X3, r2_hidden X1 X3 → r2_hidden X1 X2 → r1_xboole_0 X2 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) → (∀X1 X2, (v1_xboole_0 X2 → False) → r1_xboole_0 X1 X2 → r2_hidden X1 (esk16_1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 (k3_tarski X2) → False) → r2_hidden X1 (esk11_1 X2) → False) → (∀X1 X2, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk18_2 X1 X2) X1 → False) → False) → (∀X2 X1, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk18_2 X1 X2) X2 → False) → 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, r2_hidden X1 esk1_0 → r1_xboole_0 (esk2_1 X1) esk1_0 → False) → (∀X1, (r2_hidden (esk3_1 X1) (esk4_1 X1) → False) → r2_hidden X1 esk1_0 → False) → (∀X1, (r2_hidden (esk2_1 X1) (esk3_1 X1) → False) → r2_hidden X1 esk1_0 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1, (r2_hidden (esk4_1 X1) X1 → False) → r2_hidden X1 esk1_0 → False) → (∀X2 X1, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 X1 X2 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (r1_xboole_0 (esk17_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (r2_hidden (esk17_1 X1) X1 → False) → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 esk1_0 → False) → (∀X2 X3 X1, ((k2_xboole_0 (k2_xboole_0 X1 X2) X3) = (k2_xboole_0 X1 (k2_xboole_0 X2 X3)) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → ((v1_xboole_0 esk9_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → False