% Mizar problem: t5_sheffer1,sheffer1,254,5 
fof(t5_sheffer1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v11_lattices(A) &  (v7_robbins1(A) &  (v1_sheffer1(A) &  (v2_sheffer1(A) &  (v3_sheffer1(A) &  (v4_sheffer1(A) & l3_lattices(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k4_lattices(A, B, k2_sheffer1(A))=k2_sheffer1(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_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_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(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(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(d11_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (v11_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)) => k2_lattices(A, B, k1_lattices(A, C, D))=k1_lattices(A, k2_lattices(A, B, C), k2_lattices(A, B, D))) ) ) ) ) ) ) ) ) ).
fof(d4_sheffer1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (v2_sheffer1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (B=k2_sheffer1(A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (k1_lattices(A, B, C)=C & k1_lattices(A, C, B)=C) ) ) ) ) ) ) ) ) ).
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_k2_sheffer1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => m1_subset_1(k2_sheffer1(A), 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_k3_sheffer1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k3_sheffer1(A, B), 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_k5_ordinal1, axiom, $true).
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(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(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_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, 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_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(t3_sheffer1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v11_lattices(A) &  (v1_sheffer1(A) &  (v3_sheffer1(A) &  (v4_sheffer1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k4_lattices(A, B, k3_sheffer1(A, B))=k2_sheffer1(A)) ) ) ) ).
