% Mizar problem: t117_absred_0,absred_0,1735,7 
fof(t117_absred_0, conjecture,  (! [A] :  (l1_absred_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v4_absred_0(A) & v6_absred_0(A))  => r9_absred_0(A, k3_absred_0(A, B), B)) ) ) ) ) ).
fof(cc1_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v2_absred_0(B, A) => v3_absred_0(B, A)) ) ) ) ) ).
fof(cc3_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  (v8_absred_0(A) => v6_absred_0(A)) ) ) ).
fof(cc4_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  (v8_absred_0(A) => v7_absred_0(A)) ) ) ).
fof(cc5_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  (v7_absred_0(A) => v6_absred_0(A)) ) ) ).
fof(cc6_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  ( (v4_absred_0(A) & v6_absred_0(A))  => v8_absred_0(A)) ) ) ).
fof(cc7_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  ( (v4_absred_0(A) & v6_absred_0(A))  => v7_absred_0(A)) ) ) ).
fof(d12_absred_0, axiom,  (! [A] :  (l1_absred_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r9_absred_0(A, B, C) <=>  (v2_absred_0(B, A) & r3_absred_0(A, C, B)) ) ) ) ) ) ) ) ).
fof(d19_absred_0, axiom,  (! [A] :  (l1_absred_0(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)) =>  ( (r9_absred_0(A, C, B) & r9_absred_0(A, D, B))  => C=D) ) ) ) )  =>  ( (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ (r9_absred_0(A, C, B)) ) )  |  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (C=k3_absred_0(A, B) <=> r9_absred_0(A, C, B)) ) ) ) ) ) ) ) ) ).
fof(dt_k3_absred_0, axiom,  (! [A, B] :  ( (l1_absred_0(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k3_absred_0(A, B), u1_struct_0(A))) ) ).
fof(dt_l1_absred_0, axiom,  (! [A] :  (l1_absred_0(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_absred_0, axiom,  (? [A] : l1_absred_0(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(reflexivity_r3_absred_0, axiom,  (! [A, B, C] :  ( (l1_absred_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_absred_0(A, B, B)) ) ).
