% Mizar problem: t14_nelson_1,nelson_1,448,7 
fof(t14_nelson_1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v15_lattices(A) &  (v3_nelson_1(A) &  (v4_nelson_1(A) &  (v5_nelson_1(A) &  (v6_nelson_1(A) &  (v7_nelson_1(A) &  (v8_nelson_1(A) &  (v9_nelson_1(A) &  (v10_nelson_1(A) &  (v11_nelson_1(A) &  (v12_nelson_1(A) &  (v13_nelson_1(A) &  (v14_nelson_1(A) &  (v15_nelson_1(A) &  (v16_nelson_1(A) & l1_nelson_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k4_lattices(A, k4_lattices(A, B, k3_robbins1(A, B)), k3_lattices(A, C, k3_robbins1(A, C)))=k4_lattices(A, B, k3_robbins1(A, B))) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v19_lattices(B, A) => v21_lattices(B, A)) ) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_robbins3, axiom,  (! [A] :  (l4_robbins1(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v8_robbins1(A) &  (v10_robbins1(A) &  (v8_robbins3(A) & v9_robbins3(A)) ) ) ) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v11_lattices(A)) ) ) ) ).
fof(cc1_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v1_lattice2(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v13_lattices(A) & v3_filter_0(A)) ) ) ) ) ) ).
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(cc1_nelson_1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_robbins1(A) & v8_robbins3(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_nelson_1(A)) ) ) ) ).
fof(cc1_robbins3, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_robbins3(A) &  (v2_robbins3(A) & v3_robbins3(A)) ) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_zfmisc_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_zfmisc_1(A)) ) ).
fof(cc2_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_robbins3(A) &  (v1_lattad_1(A) &  (v2_lattad_1(A) & v3_lattad_1(A)) ) ) ) ) ) ) ).
fof(cc2_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v13_lattices(A) & v3_filter_0(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v1_lattice2(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(cc2_nelson_1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_robbins3(A) & v1_nelson_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v10_robbins1(A)) ) ) ) ).
fof(cc2_robbins3, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v9_lattices(A) &  (v1_robbins3(A) &  (v2_robbins3(A) & v3_robbins3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc3_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc3_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & v10_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v13_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(cc3_nelson_1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v1_nelson_1(A)) ) ) ) ).
fof(cc4_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ).
fof(cc4_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & v10_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v14_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(cc4_nelson_1, axiom,  (! [A] :  (l1_nelson_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v15_lattices(A) & v5_nelson_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v11_lattices(A) &  (v15_lattices(A) &  (v8_robbins3(A) & v1_nelson_1(A)) ) ) ) ) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc5_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v5_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc5_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & v10_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v15_lattices(A)) ) ) ) ) ).
fof(cc5_nelson_1, axiom,  (! [A] :  (l1_nelson_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v11_lattices(A) &  (v15_lattices(A) &  (v8_robbins3(A) & v1_nelson_1(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v15_lattices(A) & v5_nelson_1(A)) ) ) ) ) ) ).
fof(cc5_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v10_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v6_lattices(A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v5_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc6_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v10_lattices(A) & v11_lattices(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v1_lattice2(A)) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(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(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc8_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v6_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc9_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v18_lattices(B, A) => v20_lattices(B, A)) ) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(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(d19_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_nelson_1(A))  =>  (v15_nelson_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => r1_nelson_1(A, k2_lattices(A, B, k3_robbins1(A, B)), C)) ) ) ) ) ) ) ).
fof(d2_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_nelson_1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_nelson_1(A, B, C)=k4_binop_1(u1_struct_0(A), u3_nelson_1(A), B, C)) ) ) ) ) ) ).
fof(d3_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_nelson_1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_nelson_1(A, B, C) <=> k1_nelson_1(A, B, C)=k6_lattices(A)) ) ) ) ) ) ) ).
fof(d4_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_nelson_1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_nelson_1(A, B, C) <=> B=k2_lattices(A, B, C)) ) ) ) ) ) ) ).
fof(d6_robbins3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_robbins1(A))  =>  (v8_robbins3(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k3_robbins1(A, k3_robbins1(A, B))=B) ) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
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_k1_nelson_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_nelson_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_nelson_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
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_k2_zfmisc_1, axiom, $true).
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_k3_robbins1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_robbins1(A))  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k3_robbins1(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), 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_k5_ordinal1, axiom, $true).
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_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_nelson_1, axiom,  (! [A] :  (l1_nelson_1(A) => l4_robbins1(A)) ) ).
fof(dt_l1_robbins1, axiom,  (! [A] :  (l1_robbins1(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_l2_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  (l2_lattices(A) & l1_robbins1(A)) ) ) ).
fof(dt_l3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (l1_lattices(A) & l2_lattices(A)) ) ) ).
fof(dt_l4_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  (l2_robbins1(A) & l3_lattices(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u3_nelson_1, axiom,  (! [A] :  (l1_nelson_1(A) =>  (v1_funct_1(u3_nelson_1(A)) &  (v1_funct_2(u3_nelson_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u3_nelson_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_nelson_1, axiom,  (? [A] : l1_nelson_1(A)) ).
fof(existence_l1_robbins1, axiom,  (? [A] : l1_robbins1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l2_robbins1, axiom,  (? [A] : l2_robbins1(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_l4_robbins1, axiom,  (? [A] : l4_robbins1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc3_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc4_zfmisc_1, axiom,  (! [A, B] :  ( (v1_zfmisc_1(A) & v1_zfmisc_1(B))  => v1_zfmisc_1(k2_zfmisc_1(A, B))) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(rc14_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc15_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc1_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & v10_lattices(A)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_lattice2, 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) &  (v10_lattices(A) & v1_lattice2(A)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_nelson_1, axiom,  (? [A] :  (l4_robbins1(A) &  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v11_lattices(A) &  (v15_lattices(A) &  (v8_robbins3(A) & v1_nelson_1(A)) ) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_zfmisc_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v11_lattices(A) &  (v3_robbins3(A) &  (v1_lattad_1(A) &  (v2_lattad_1(A) & v3_lattad_1(A)) ) ) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_zfmisc_1, axiom,  (? [A] :  ~ (v1_zfmisc_1(A)) ) ).
fof(rc3_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ).
fof(rc4_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v6_lattad_1(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_nelson_1, axiom,  (? [A] :  (l1_nelson_1(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v10_lattices(A) &  (v11_lattices(A) &  (v15_lattices(A) &  (v8_robbins3(A) & v1_nelson_1(A)) ) ) ) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc5_nelson_1, axiom,  (? [A] :  (l1_nelson_1(A) &  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v10_lattices(A) &  (v13_lattices(A) &  (v14_lattices(A) &  (v15_lattices(A) &  (v1_robbins3(A) &  (v2_robbins3(A) &  (v3_robbins3(A) &  (v3_nelson_1(A) &  (v4_nelson_1(A) &  (v5_nelson_1(A) &  (v6_nelson_1(A) &  (v7_nelson_1(A) &  (v8_nelson_1(A) &  (v9_nelson_1(A) &  (v10_nelson_1(A) &  (v11_nelson_1(A) &  (v12_nelson_1(A) &  (v13_nelson_1(A) &  (v14_nelson_1(A) &  (v15_nelson_1(A) & v16_nelson_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v20_lattices(B, A) & v21_lattices(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(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_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
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_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t13_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v15_lattices(A) &  (v3_nelson_1(A) &  (v4_nelson_1(A) &  (v5_nelson_1(A) &  (v6_nelson_1(A) &  (v7_nelson_1(A) &  (v8_nelson_1(A) &  (v9_nelson_1(A) &  (v10_nelson_1(A) &  (v11_nelson_1(A) &  (v12_nelson_1(A) &  (v13_nelson_1(A) &  (v14_nelson_1(A) &  (v15_nelson_1(A) &  (v16_nelson_1(A) & l1_nelson_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k3_robbins1(A, k4_lattices(A, B, C))=k3_lattices(A, k3_robbins1(A, B), k3_robbins1(A, C))) ) ) ) ) ) ).
fof(t1_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v11_lattices(A) &  (v15_lattices(A) &  (v8_robbins3(A) &  (v1_nelson_1(A) & l4_robbins1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k3_robbins1(A, k3_lattices(A, B, C))=k4_lattices(A, k3_robbins1(A, B), k3_robbins1(A, C))) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t9_nelson_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v15_lattices(A) &  (v3_nelson_1(A) &  (v4_nelson_1(A) &  (v5_nelson_1(A) &  (v6_nelson_1(A) &  (v7_nelson_1(A) &  (v8_nelson_1(A) &  (v9_nelson_1(A) &  (v10_nelson_1(A) &  (v11_nelson_1(A) &  (v12_nelson_1(A) &  (v13_nelson_1(A) &  (v14_nelson_1(A) &  (v15_nelson_1(A) &  (v16_nelson_1(A) & l1_nelson_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_nelson_1(A, B, C) <=>  (r1_nelson_1(A, B, C) & r1_nelson_1(A, k3_robbins1(A, C), k3_robbins1(A, B))) ) ) ) ) ) ) ) ).
