Theorem. (
t67_boolealg)
∀k2_lattices : set → set → set → set, ∀esk5_1 : set → set, ∀k1_lattices : set → set → set → set, ∀esk7_1 : set → set, ∀esk6_1 : set → set, ∀v11_lattices : set → prop, ∀l2_lattices : set → prop, ∀esk8_1 : set → set, ∀esk10_1 : set → set, ∀esk9_1 : set → set, ∀v5_lattices : set → prop, ∀k2_boolealg : set → set → set → set, ∀k7_lattices : set → set → set, ∀v4_lattices : set → prop, ∀v12_lattices : set → prop, ∀esk14_0 : set, ∀esk17_0 : set, ∀esk16_0 : set, ∀esk15_0 : set, ∀esk18_1 : set → set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀l1_struct_0 : set → prop, ∀v14_lattices : set → prop, ∀v13_lattices : set → prop, ∀v15_lattices : set → prop, ∀v16_lattices : set → prop, ∀v9_lattices : set → prop, ∀v8_lattices : set → prop, ∀k3_boolealg : set → set → set → set, ∀v6_lattices : set → prop, ∀v7_lattices : set → prop, ∀esk12_1 : set → set, ∀esk13_1 : set → set, ∀esk11_1 : set → set, ∀l1_lattices : set → prop, ∀r1_boolealg : set → set → set → prop, ∀k3_lattices : set → set → set → set, ∀k1_boolealg : set → set → set → set, ∀k4_lattices : set → set → set → set, ∀v17_lattices : set → prop, ∀m1_subset_1 : set → set → prop, ∀u1_struct_0 : set → set, ∀l3_lattices : set → prop, ∀v10_lattices : set → prop, ∀v2_struct_0 : set → prop, (∀X3 X2 X1, (v2_struct_0 X1 → False) → (r1_boolealg X1 (k1_boolealg X1 (k3_lattices X1 X2 X3) (k4_lattices X1 X2 X3)) (k3_lattices X1 (k1_boolealg X1 X2 X3) (k1_boolealg X1 X3 X2)) → False) → v10_lattices X1 → v17_lattices X1 → l3_lattices 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 X1 → False) → (r1_boolealg X1 (k1_boolealg X1 X2 (k1_boolealg X1 X3 X4)) (k3_lattices X1 (k1_boolealg X1 X2 X3) (k4_lattices X1 X2 X4)) → False) → v10_lattices X1 → v17_lattices X1 → l3_lattices X1 → m1_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 X1 → False) → (r1_boolealg X1 (k1_boolealg X1 (k1_boolealg X1 X2 X3) X4) (k1_boolealg X1 X2 (k3_lattices X1 X3 X4)) → False) → v10_lattices X1 → v17_lattices X1 → l3_lattices X1 → m1_subset_1 X4 (u1_struct_0 X1) → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → (v11_lattices X1 → False) → (k1_lattices X1 (k2_lattices X1 (esk5_1 X1) (esk6_1 X1)) (k2_lattices X1 (esk5_1 X1) (esk7_1 X1))) = (k2_lattices X1 (esk5_1 X1) (k1_lattices X1 (esk6_1 X1) (esk7_1 X1))) → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v7_lattices X1 → False) → (k2_lattices X1 (k2_lattices X1 (esk11_1 X1) (esk12_1 X1)) (esk13_1 X1)) = (k2_lattices X1 (esk11_1 X1) (k2_lattices X1 (esk12_1 X1) (esk13_1 X1))) → l1_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v5_lattices X1 → False) → (k1_lattices X1 (k1_lattices X1 (esk8_1 X1) (esk9_1 X1)) (esk10_1 X1)) = (k1_lattices X1 (esk8_1 X1) (k1_lattices X1 (esk9_1 X1) (esk10_1 X1))) → l2_lattices X1 → False) → (∀X4 X3 X2 X1, ((k1_lattices X1 (k2_lattices X1 X2 X3) (k2_lattices X1 X2 X4)) = (k2_lattices X1 X2 (k1_lattices X1 X3 X4)) → False) → (v2_struct_0 X1 → False) → l3_lattices X1 → v11_lattices X1 → m1_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, ((k2_lattices X1 (k2_lattices X1 X2 X3) X4) = (k2_lattices X1 X2 (k2_lattices X1 X3 X4)) → False) → (v2_struct_0 X1 → False) → v7_lattices X1 → l1_lattices X1 → m1_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_lattices X1 (k1_lattices X1 X2 X3) X4) = (k1_lattices X1 X2 (k1_lattices X1 X3 X4)) → False) → (v2_struct_0 X1 → False) → v5_lattices X1 → l2_lattices X1 → m1_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, ((k3_lattices X1 (k1_boolealg X1 X2 X3) (k1_boolealg X1 X3 X2)) = (k2_boolealg X1 X2 X3) → False) → (v2_struct_0 X1 → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (r1_boolealg X1 X3 X2 → False) → v10_lattices X1 → l3_lattices X1 → r1_boolealg X1 X2 X3 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k4_lattices X1 X2 (k7_lattices X1 X3)) = (k1_boolealg X1 X2 X3) → False) → (v2_struct_0 X1 → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k2_boolealg X1 X2 X3) (u1_struct_0 X1) → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k1_boolealg X1 X2 X3) (u1_struct_0 X1) → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k4_lattices X1 X2 X3) (u1_struct_0 X1) → False) → v6_lattices X1 → l1_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k3_lattices X1 X2 X3) (u1_struct_0 X1) → False) → v4_lattices X1 → l2_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k3_boolealg X1 X2 X3) (u1_struct_0 X1) → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X3 X2 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k2_lattices X1 X2 X3) (u1_struct_0 X1) → False) → l1_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X3 X2 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k1_lattices X1 X2 X3) (u1_struct_0 X1) → False) → l2_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k2_boolealg X1 X2 X3) = (k3_boolealg X1 X2 X3) → False) → (v2_struct_0 X1 → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k4_lattices X1 X2 X3) = (k2_lattices X1 X2 X3) → False) → (v2_struct_0 X1 → False) → v6_lattices X1 → l1_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k3_lattices X1 X2 X3) = (k1_lattices X1 X2 X3) → False) → (v2_struct_0 X1 → False) → v4_lattices X1 → l2_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k4_lattices X1 X2 X3) = (k4_lattices X1 X3 X2) → False) → (v2_struct_0 X1 → False) → v6_lattices X1 → l1_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k3_lattices X1 X2 X3) = (k3_lattices X1 X3 X2) → False) → (v2_struct_0 X1 → False) → v4_lattices X1 → l2_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X3 X1, ((k3_boolealg X1 X2 X3) = (k3_boolealg X1 X3 X2) → False) → (v2_struct_0 X1 → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X1 X2 X3, (X2 = X3 → False) → (v2_struct_0 X1 → False) → v10_lattices X1 → l3_lattices X1 → r1_boolealg X1 X2 X3 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X1 X3, (v2_struct_0 X3 → False) → (r1_boolealg X3 X1 X2 → False) → X1 = X2 → v10_lattices X3 → l3_lattices X3 → m1_subset_1 X2 (u1_struct_0 X3) → m1_subset_1 X1 (u1_struct_0 X3) → False) → (∀X2 X3 X1, (v2_struct_0 X1 → False) → (r1_boolealg X1 X2 X2 → False) → v10_lattices X1 → l3_lattices X1 → m1_subset_1 X3 (u1_struct_0 X1) → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X1, ((k1_lattices X1 X2 X2) = X2 → False) → (v2_struct_0 X1 → False) → l3_lattices X1 → v6_lattices X1 → v8_lattices X1 → v9_lattices X1 → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X1, ((k4_lattices X1 X2 X2) = X2 → False) → (v2_struct_0 X1 → False) → l3_lattices X1 → v6_lattices X1 → v8_lattices X1 → v9_lattices X1 → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X1, ((k7_lattices X1 (k7_lattices X1 X2)) = X2 → False) → (v2_struct_0 X1 → False) → v10_lattices X1 → v17_lattices X1 → l3_lattices X1 → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X2 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (k7_lattices X1 X2) (u1_struct_0 X1) → False) → l3_lattices X1 → m1_subset_1 X2 (u1_struct_0 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → (v10_lattices X1 → False) → l3_lattices X1 → v4_lattices X1 → v5_lattices X1 → v6_lattices X1 → v7_lattices X1 → v8_lattices X1 → v9_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v11_lattices X1 → False) → (m1_subset_1 (esk7_1 X1) (u1_struct_0 X1) → False) → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v11_lattices X1 → False) → (m1_subset_1 (esk6_1 X1) (u1_struct_0 X1) → False) → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v11_lattices X1 → False) → (m1_subset_1 (esk5_1 X1) (u1_struct_0 X1) → False) → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v7_lattices X1 → False) → (m1_subset_1 (esk13_1 X1) (u1_struct_0 X1) → False) → l1_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v7_lattices X1 → False) → (m1_subset_1 (esk12_1 X1) (u1_struct_0 X1) → False) → l1_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v7_lattices X1 → False) → (m1_subset_1 (esk11_1 X1) (u1_struct_0 X1) → False) → l1_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v5_lattices X1 → False) → (m1_subset_1 (esk10_1 X1) (u1_struct_0 X1) → False) → l2_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v5_lattices X1 → False) → (m1_subset_1 (esk9_1 X1) (u1_struct_0 X1) → False) → l2_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v5_lattices X1 → False) → (m1_subset_1 (esk8_1 X1) (u1_struct_0 X1) → False) → l2_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v17_lattices X1 → False) → l3_lattices X1 → v15_lattices X1 → v11_lattices X1 → v16_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v12_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → v11_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v15_lattices X1 → False) → l3_lattices X1 → v13_lattices X1 → v14_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v16_lattices X1 → False) → v17_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v11_lattices X1 → False) → v17_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v15_lattices X1 → False) → v17_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v14_lattices X1 → False) → l3_lattices X1 → v15_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v13_lattices X1 → False) → l3_lattices X1 → v15_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v9_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v8_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v7_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v6_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v5_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v4_lattices X1 → False) → v10_lattices X1 → l3_lattices X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l1_lattices X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l2_lattices X1 → False) → (∀X1, (l1_lattices X1 → False) → l3_lattices X1 → False) → (∀X1, (l2_lattices X1 → False) → l3_lattices X1 → False) → (r1_boolealg esk1_0 (k3_boolealg esk1_0 (k3_boolealg esk1_0 esk2_0 esk3_0) esk4_0) (k3_boolealg esk1_0 esk2_0 (k3_boolealg esk1_0 esk3_0 esk4_0)) → False) → (v2_struct_0 esk1_0 → False) → (∀X1, (m1_subset_1 (esk18_1 X1) X1 → 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) → ((l1_struct_0 esk15_0 → False) → False) → ((l1_lattices esk14_0 → False) → False) → ((l2_lattices esk16_0 → False) → False) → ((l3_lattices esk17_0 → False) → False) → ((l3_lattices esk1_0 → False) → False) → ((v17_lattices esk1_0 → False) → False) → ((v10_lattices esk1_0 → False) → False) → False