% Mizar problem: t12_gtarski4,gtarski4,264,7 
fof(t12_gtarski4, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(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)) => r9_gtarski3(A, k3_gtarski3(A, D, C), k3_gtarski3(A, D, k3_gtarski3(A, B, C)), k3_gtarski3(A, D, B))) ) ) ) ) ) ) ) ).
fof(cc13_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski1(A) => v2_gtarski3(A)) ) ) ).
fof(cc14_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski1(A) => v3_gtarski3(A)) ) ) ).
fof(cc15_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski1(A) => v4_gtarski3(A)) ) ) ).
fof(cc16_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski1(A) => v5_gtarski3(A)) ) ) ).
fof(cc17_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski1(A) => v7_gtarski3(A)) ) ) ).
fof(cc18_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski1(A) => v8_gtarski3(A)) ) ) ).
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(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(cc3_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski3(A) => v2_gtarski1(A)) ) ) ).
fof(cc4_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski3(A) => v3_gtarski1(A)) ) ) ).
fof(cc5_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski3(A) => v4_gtarski1(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(cc6_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski3(A) => v5_gtarski1(A)) ) ) ).
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(cc7_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski3(A) => v7_gtarski1(A)) ) ) ).
fof(cc8_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski3(A) => v8_gtarski1(A)) ) ) ).
fof(d12_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)) =>  (r9_gtarski3(A, B, C, D) <=>  (r1_gtarski1(A, B, D, C) & r2_gtarski1(A, D, B, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(d13_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_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)) =>  (D=k3_gtarski3(A, B, C) <=> r9_gtarski3(A, C, D, B)) ) ) ) ) ) ) ) ) ).
fof(dt_k3_gtarski3, axiom,  (! [A, B, C] :  ( ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & l1_gtarski1(A)) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_gtarski3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_l1_gtarski1, axiom,  (! [A] :  (l1_gtarski1(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_gtarski1, axiom,  (? [A] : l1_gtarski1(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(rc3_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski3(A) & v3_gtarski3(A)) ) ) ).
fof(rc5_gtarski1, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  & v9_gtarski1(A)) ) ) ).
fof(rc5_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v3_gtarski3(A) & v5_gtarski3(A)) ) ) ).
fof(t106_gtarski3, axiom,  (! [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)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r1_gtarski1(A, C, D, E) <=> r1_gtarski1(A, k3_gtarski3(A, B, C), k3_gtarski3(A, B, D), k3_gtarski3(A, B, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t107_gtarski3, axiom,  (! [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)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (r2_gtarski1(A, C, D, E, F) <=> r2_gtarski1(A, k3_gtarski3(A, B, C), k3_gtarski3(A, B, D), k3_gtarski3(A, B, E), k3_gtarski3(A, B, F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
