% Mizar problem: t36_boolealg,boolealg,369,5 
fof(t36_boolealg, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v17_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => r1_boolealg(A, k3_lattices(A, k4_lattices(A, B, C), k1_boolealg(A, B, C)), B)) ) ) ) ) ) ).
fof(cc1_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) ) ) ) ) ).
fof(cc2_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  & v15_lattices(A)) ) ) ) ).
fof(cc4_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v15_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(A)) ) ) ) ) ).
fof(cc5_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v17_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v11_lattices(A) &  (v15_lattices(A) & v16_lattices(A)) ) ) ) ) ) ).
fof(cc6_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v11_lattices(A) &  (v15_lattices(A) & v16_lattices(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v17_lattices(A)) ) ) ) ).
fof(cc7_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v11_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v12_lattices(A)) ) ) ) ) ).
fof(commutativity_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_lattices(A, B, C)=k3_lattices(A, C, B)) ) ).
fof(commutativity_k4_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) & l1_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k4_lattices(A, B, C)=k4_lattices(A, C, B)) ) ).
fof(d1_boolealg, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_boolealg(A, B, C)=k4_lattices(A, B, k7_lattices(A, C))) ) ) ) ) ) ).
fof(d3_boolealg, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_boolealg(A, B, C) <=>  (r3_lattices(A, B, C) & r3_lattices(A, C, B)) ) ) ) ) ) ) ) ).
fof(d8_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (v8_lattices(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_lattices(A, k2_lattices(A, B, C), C)=C) ) ) ) ) ) ) ).
fof(d9_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (v9_lattices(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_lattices(A, B, k1_lattices(A, B, C))=B) ) ) ) ) ) ) ).
fof(dt_k1_boolealg, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_boolealg(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k4_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) & l1_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k6_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  => m1_subset_1(k6_lattices(A), u1_struct_0(A))) ) ).
fof(dt_k7_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) ) ).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_lattices, axiom,  (! [A] :  (l2_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (l1_lattices(A) & l2_lattices(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(rd1_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k1_lattices(A, B, B)=B) ) ).
fof(rd2_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k4_lattices(A, B, B)=B) ) ).
fof(rd5_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v14_lattices(A) & l3_lattices(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k4_lattices(A, k6_lattices(A), B)=B) ) ).
fof(rd6_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v14_lattices(A) & l3_lattices(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k3_lattices(A, k6_lattices(A), B)=k6_lattices(A)) ) ).
fof(rd7_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v17_lattices(A) & l3_lattices(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k7_lattices(A, k7_lattices(A, B))=B) ) ).
fof(redefinition_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_lattices(A, B, C)=k1_lattices(A, B, C)) ) ).
fof(redefinition_k4_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) & l1_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k4_lattices(A, B, C)=k2_lattices(A, B, C)) ) ).
fof(redefinition_r1_boolealg, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r1_boolealg(A, B, C) <=> B=C) ) ) ).
fof(redefinition_r3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) ) ) ).
fof(reflexivity_r1_boolealg, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r1_boolealg(A, B, B)) ) ).
fof(reflexivity_r3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_lattices(A, B, B)) ) ).
fof(symmetry_r1_boolealg, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r1_boolealg(A, B, C) => r1_boolealg(A, C, B)) ) ) ).
fof(t11_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v11_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k3_lattices(A, B, k4_lattices(A, C, D))=k4_lattices(A, k3_lattices(A, B, C), k3_lattices(A, B, D))) ) ) ) ) ) ) ) ).
fof(t21_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v17_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k3_lattices(A, k7_lattices(A, B), B)=k6_lattices(A)) ) ) ) ).
