% Mizar problem: t58_robbins2,robbins2,661,5 
fof(t58_robbins2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_robbins1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( (v4_lattices(A) &  (v5_lattices(A) & v6_robbins1(A)) )  => k4_robbins1(A, k1_lattices(A, C, B), k1_lattices(A, C, k3_robbins1(A, B)))=C) ) ) ) ) ) ) ).
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_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_robbins1(A) & v7_robbins1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v14_lattices(A)) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc2_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v6_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v7_robbins1(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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(commutativity_k5_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_robbins1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k5_robbins1(A, B, C)=k5_robbins1(A, C, B)) ) ).
fof(commutativity_k6_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & l2_robbins1(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k6_robbins1(A, B, C)=k6_robbins1(A, C, B)) ) ).
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_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_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l2_robbins1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k4_robbins1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_robbins1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_robbins1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k6_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & l2_robbins1(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k6_robbins1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k7_robbins1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_robbins1(A) &  (v7_robbins1(A) & l2_robbins1(A)) ) ) ) )  => m1_subset_1(k7_robbins1(A), u1_struct_0(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_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
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_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(redefinition_k5_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_robbins1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k5_robbins1(A, B, C)=k1_lattices(A, B, C)) ) ).
fof(redefinition_k6_robbins1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & l2_robbins1(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k6_robbins1(A, B, C)=k4_robbins1(A, B, C)) ) ).
fof(t13_robbins1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_robbins1(A) & l2_robbins1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k5_robbins1(A, B, k7_robbins1(A))=B) ) ) ) ).
fof(t15_robbins1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_robbins1(A) & l2_robbins1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k6_robbins1(A, B, k3_robbins1(A, B))=k7_robbins1(A)) ) ) ) ).
fof(t31_robbins1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_robbins1(A) & l2_robbins1(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_robbins1(A, B, k6_robbins1(A, C, D))=k6_robbins1(A, k5_robbins1(A, B, C), k5_robbins1(A, B, D))) ) ) ) ) ) ) ) ).
