% Mizar problem: l27_lattba_1,lattba_1,437,7 
fof(l27_lattba_1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_lattba_1(A) &  (v4_lattba_1(A) &  (v5_lattba_1(A) &  (v6_lattba_1(A) &  (v7_lattba_1(A) & l1_lattba_1(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)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k4_binop_1(u1_struct_0(A), k3_lattba_1(A, B), k4_binop_1(u1_struct_0(A), k3_lattba_1(A, B), C, D), E)=k4_binop_1(u1_struct_0(A), k3_lattba_1(A, B), C, k4_binop_1(u1_struct_0(A), k3_lattba_1(A, B), D, E))) ) ) ) ) ) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_lattba_1, axiom,  (! [A] :  (l1_lattba_1(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_lattba_1(A) &  (v4_lattba_1(A) &  (v5_lattba_1(A) &  (v6_lattba_1(A) & v7_lattba_1(A)) ) ) ) ) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(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_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(d2_lattba_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lattba_1(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)) => k2_lattba_1(A, B, C, D)=k2_multop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattba_1(A), B, C, D)) ) ) ) ) ) ) ) ).
fof(d8_lattba_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_lattba_1(A) &  (v4_lattba_1(A) &  (v5_lattba_1(A) &  (v6_lattba_1(A) &  (v7_lattba_1(A) & l1_lattba_1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) )  =>  (C=k3_lattba_1(A, B) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k4_binop_1(u1_struct_0(A), C, D, E)=k2_lattba_1(A, D, B, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_multop_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_lattba_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  & l1_lattba_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) & m1_subset_1(D, u1_struct_0(A))) ) )  => m1_subset_1(k2_lattba_1(A, B, C, D), u1_struct_0(A))) ) ).
fof(dt_k2_multop_1, axiom,  (! [A, B, C, D, E, F, G, H] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, k3_zfmisc_1(A, B, C), D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k3_zfmisc_1(A, B, C), D)))) )  &  (m1_subset_1(F, A) &  (m1_subset_1(G, B) & m1_subset_1(H, C)) ) ) ) ) ) )  => m1_subset_1(k2_multop_1(A, B, C, D, E, F, G, H), D)) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_lattba_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_lattba_1(A) &  (v4_lattba_1(A) &  (v5_lattba_1(A) &  (v6_lattba_1(A) &  (v7_lattba_1(A) & l1_lattba_1(A)) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (v1_funct_1(k3_lattba_1(A, B)) &  (v1_funct_2(k3_lattba_1(A, B), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(k3_lattba_1(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_k3_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_l1_lattba_1, axiom,  (! [A] :  (l1_lattba_1(A) => l1_robbins1(A)) ) ).
fof(dt_l1_robbins1, axiom,  (! [A] :  (l1_robbins1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_lattba_1, axiom,  (! [A] :  (l1_lattba_1(A) =>  (v1_funct_1(u1_lattba_1(A)) &  (v1_funct_2(u1_lattba_1(A), k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_lattba_1(A), k1_zfmisc_1(k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_lattba_1, axiom,  (? [A] : l1_lattba_1(A)) ).
fof(existence_l1_robbins1, axiom,  (? [A] : l1_robbins1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc3_lattba_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_lattba_1(A) &  (v4_lattba_1(A) &  (v5_lattba_1(A) &  (v6_lattba_1(A) &  (v7_lattba_1(A) & l1_lattba_1(A)) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (v1_funct_1(k3_lattba_1(A, B)) &  (v1_funct_2(k3_lattba_1(A, B), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v1_binop_1(k3_lattba_1(A, B), u1_struct_0(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(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_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(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_lattba_1, axiom,  (? [A] :  (l1_lattba_1(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(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(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(redefinition_k2_multop_1, axiom,  (! [A, B, C, D, E, F, G, H] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, k3_zfmisc_1(A, B, C), D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k3_zfmisc_1(A, B, C), D)))) )  &  (m1_subset_1(F, A) &  (m1_subset_1(G, B) & m1_subset_1(H, C)) ) ) ) ) ) )  => k2_multop_1(A, B, C, D, E, F, G, H)=k1_multop_1(E, F, G, H)) ) ).
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(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
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_lattba_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_lattba_1(A) &  (v4_lattba_1(A) &  (v5_lattba_1(A) &  (v6_lattba_1(A) &  (v7_lattba_1(A) & l1_lattba_1(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)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k2_lattba_1(A, B, C, k2_lattba_1(A, D, C, E))=k2_lattba_1(A, k2_lattba_1(A, B, C, D), C, E)) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
