% Mizar problem: t16_quantal1,quantal1,881,5 
fof(t16_quantal1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) &  (v3_group_1(A) &  (v7_quantal1(A) &  (v8_quantal1(A) & l1_quantal1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (v18_quantal1(B, A) =>  (r3_lattices(A, C, k1_quantal1(A, k1_quantal1(A, C, B), B)) & r3_lattices(A, C, k2_quantal1(A, k2_quantal1(A, C, B), 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_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_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, 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(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, 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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
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(d15_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_quantal1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_quantal1(A, B, C)=k15_lattice3(A, a_3_6_quantal1(A, B, C))) ) ) ) ) ) ).
fof(d16_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_quantal1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_quantal1(A, B, C)=k15_lattice3(A, a_3_7_quantal1(A, B, C))) ) ) ) ) ) ).
fof(d18_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k6_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u2_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d1_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_lattices(A, B, C)=k4_binop_1(u1_struct_0(A), u2_lattices(A), B, C)) ) ) ) ) ) ).
fof(d3_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_lattices(A, B, C) <=> k1_lattices(A, B, C)=C) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k15_lattice3, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => m1_subset_1(k15_lattice3(A, B), u1_struct_0(A))) ) ).
fof(dt_k16_lattice3, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => m1_subset_1(k16_lattice3(A, B), u1_struct_0(A))) ) ).
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_quantal1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_quantal1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_quantal1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_quantal1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_quantal1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_quantal1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
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_k5_ordinal1, axiom, $true).
fof(dt_k6_algstr_0, axiom,  (! [A, B, C] :  ( (l3_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k6_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_quantal1, axiom,  (! [A] :  (l1_quantal1(A) =>  (l3_lattices(A) & l3_algstr_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_algstr_0, axiom,  (! [A] :  (l3_algstr_0(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(dt_u2_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u2_lattices, axiom,  (! [A] :  (l2_lattices(A) =>  (v1_funct_1(u2_lattices(A)) &  (v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_lattices(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_quantal1, axiom,  (? [A] : l1_quantal1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(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(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_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(fraenkel_a_2_3_lattice3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) &  (v4_lattice3(B) & l3_lattices(B)) ) )  & m1_subset_1(C, u1_struct_0(B)))  =>  (r2_hidden(A, a_2_3_lattice3(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=D & r3_lattices(B, D, C)) ) ) ) ) ) ).
fof(fraenkel_a_2_3_quantal1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) &  (v4_lattice3(B) &  (v3_group_1(B) &  (v7_quantal1(B) &  (v8_quantal1(B) & l1_quantal1(B)) ) ) ) ) )  & m1_subset_1(C, u1_struct_0(B)))  =>  (r2_hidden(A, a_2_3_quantal1(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=D & r3_lattices(B, D, C)) ) ) ) ) ) ).
fof(fraenkel_a_2_4_lattice3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) &  (v4_lattice3(B) & l3_lattices(B)) ) )  & m1_subset_1(C, u1_struct_0(B)))  =>  (r2_hidden(A, a_2_4_lattice3(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=D & r3_lattices(B, C, D)) ) ) ) ) ) ).
fof(fraenkel_a_3_23_quantal1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) &  (v4_lattice3(B) &  (v3_group_1(B) &  (v7_quantal1(B) &  (v8_quantal1(B) & l1_quantal1(B)) ) ) ) ) )  &  (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_23_quantal1(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=E & r3_lattices(B, k6_algstr_0(B, E, k1_quantal1(B, D, C)), C)) ) ) ) ) ) ).
fof(fraenkel_a_3_24_quantal1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) &  (v4_lattice3(B) &  (v3_group_1(B) &  (v7_quantal1(B) &  (v8_quantal1(B) & l1_quantal1(B)) ) ) ) ) )  &  (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_24_quantal1(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=E & r3_lattices(B, k6_algstr_0(B, k2_quantal1(B, D, C), E), C)) ) ) ) ) ) ).
fof(fraenkel_a_3_6_quantal1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l1_quantal1(B))  &  (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_6_quantal1(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=E & r1_lattices(B, k6_algstr_0(B, E, C), D)) ) ) ) ) ) ).
fof(fraenkel_a_3_7_quantal1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l1_quantal1(B))  &  (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_7_quantal1(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=E & r1_lattices(B, k6_algstr_0(B, C, E), D)) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(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_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(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_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_quantal1, axiom,  (? [A] :  (l1_quantal1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
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(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_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
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_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t11_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) &  (v3_group_1(A) &  (v7_quantal1(A) &  (v8_quantal1(A) & l1_quantal1(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)) =>  (r3_lattices(A, k6_algstr_0(A, B, C), D) <=> r3_lattices(A, C, k2_quantal1(A, B, D))) ) ) ) ) ) ) ) ) ).
fof(t12_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) &  (v3_group_1(A) &  (v7_quantal1(A) &  (v8_quantal1(A) & l1_quantal1(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)) =>  (r3_lattices(A, k6_algstr_0(A, B, C), D) <=> r3_lattices(A, B, k1_quantal1(A, C, D))) ) ) ) ) ) ) ) ) ).
fof(t13_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) &  (v3_group_1(A) &  (v7_quantal1(A) &  (v8_quantal1(A) & l1_quantal1(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)) =>  (r3_lattices(A, C, D) =>  (r3_lattices(A, k1_quantal1(A, D, B), k1_quantal1(A, C, B)) & r3_lattices(A, k2_quantal1(A, D, B), k2_quantal1(A, C, B))) ) ) ) ) ) ) ) ) ) ).
fof(t15_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) &  (v3_group_1(A) &  (v7_quantal1(A) &  (v8_quantal1(A) & l1_quantal1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v18_quantal1(B, A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r3_lattices(A, k6_algstr_0(A, C, D), B) => r3_lattices(A, k6_algstr_0(A, D, C), B)) ) ) ) ) ) ) ) ) ) ).
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(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t44_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (B=k15_lattice3(A, a_2_3_lattice3(A, B)) & B=k16_lattice3(A, a_2_4_lattice3(A, B))) ) ) ) ) ).
fof(t45_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) & l3_lattices(A)) ) )  =>  (! [B] :  (! [C] :  (r1_tarski(B, C) =>  (r3_lattices(A, k15_lattice3(A, B), k15_lattice3(A, C)) & r3_lattices(A, k16_lattice3(A, C), k16_lattice3(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(t7_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) & l2_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)) =>  ( (r1_lattices(A, B, C) & r1_lattices(A, C, D))  => r1_lattices(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_quantal1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) &  (v3_group_1(A) &  (v7_quantal1(A) &  (v8_quantal1(A) & l1_quantal1(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)) =>  (r3_lattices(A, B, C) =>  (r3_lattices(A, k6_algstr_0(A, B, D), k6_algstr_0(A, C, D)) & r3_lattices(A, k6_algstr_0(A, D, B), k6_algstr_0(A, D, C))) ) ) ) ) ) ) ) ) ) ).
