% Mizar problem: t29_sheffer2,sheffer2,300,5 
fof(t29_sheffer2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_sheffer2(A) & l1_sheffer1(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)) => k5_sheffer1(A, k5_sheffer1(A, B, k5_sheffer1(A, C, D)), k5_sheffer1(A, B, k5_sheffer1(A, E, k5_sheffer1(A, C, B))))=k5_sheffer1(A, k5_sheffer1(A, B, k5_sheffer1(A, C, D)), k5_sheffer1(A, C, B))) ) ) ) ) ) ) ) ) ) ).
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_sheffer2, axiom,  (! [A] :  (l1_sheffer1(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v1_sheffer2(A)) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc3_sheffer1, axiom,  (! [A] :  (l1_sheffer1(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v10_sheffer1(A) &  (v11_sheffer1(A) & v12_sheffer1(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_sheffer1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_sheffer1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_sheffer1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_l1_sheffer1, axiom,  (! [A] :  (l1_sheffer1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_sheffer1, axiom,  (? [A] : l1_sheffer1(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(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(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(rc1_sheffer2, axiom,  (? [A] :  (l1_sheffer1(A) &  ( ~ (v2_struct_0(A))  &  (v10_sheffer1(A) &  (v11_sheffer1(A) &  (v12_sheffer1(A) & v1_sheffer2(A)) ) ) ) ) ) ).
fof(rc5_sheffer1, axiom,  (? [A] :  (l1_sheffer1(A) & v13_struct_0(A, 1)) ) ).
fof(t17_sheffer2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_sheffer2(A) & l1_sheffer1(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)) => k5_sheffer1(A, B, k5_sheffer1(A, k5_sheffer1(A, B, C), k5_sheffer1(A, D, C)))=k5_sheffer1(A, B, C)) ) ) ) ) ) ) ) ).
fof(t25_sheffer2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_sheffer2(A) & l1_sheffer1(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)) => k5_sheffer1(A, k5_sheffer1(A, B, k5_sheffer1(A, C, D)), k5_sheffer1(A, C, B))=B) ) ) ) ) ) ) ) ).
