% Mizar problem: t75_gtarski3,gtarski3,1511,29 
fof(t75_gtarski3, conjecture,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(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)) =>  (r7_gtarski3(A, B, C, D) => r7_gtarski3(A, C, B, D)) ) ) ) ) ) ) ) ) ).
fof(cc1_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & v1_gtarski3(A)) )  =>  (v2_gtarski1(A) &  (v3_gtarski1(A) & v6_gtarski1(A)) ) ) ) ) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(dt_l1_struct_0, axiom, $true).
fof(cc2_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & v6_gtarski1(A)) )  =>  (v2_gtarski1(A) &  (v3_gtarski1(A) & v1_gtarski3(A)) ) ) ) ) ).
fof(cc6_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & v8_gtarski1(A)) ) ) ) ) )  => v9_gtarski1(A)) ) ) ).
fof(existence_l1_gtarski1, axiom,  (? [A] : l1_gtarski1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(dt_l1_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(cc7_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v9_gtarski1(A) =>  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & v8_gtarski1(A)) ) ) ) ) ) ) ) ) ).
fof(d8_gtarski3, axiom,  (! [A] :  (l1_gtarski1(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)) =>  (r7_gtarski3(A, B, C, D) <=>  ( ~ (D=B)  &  ( ~ (D=C)  &  (r1_gtarski1(A, D, B, C) | r1_gtarski1(A, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ).
