% Mizar problem: t5_gtarski4,gtarski4,144,7 
fof(t5_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)) =>  ~ ( ( ~ (B=C)  &  ( ~ (B=D)  &  ( ~ ( ( ~ (r6_gtarski1(A, B, C, D))  &  ( ~ (r6_gtarski1(A, C, D, B))  &  ( ~ (r6_gtarski1(A, D, B, C))  &  ( ~ (r6_gtarski1(A, B, D, C))  &  ( ~ (r6_gtarski1(A, C, B, D))  &  ~ (r6_gtarski1(A, D, C, B)) ) ) ) ) ) )  &  ~ ( (k1_gtarski4(A, B, C)=k1_gtarski4(A, B, D) &  (k1_gtarski4(A, B, C)=k1_gtarski4(A, D, B) &  (k1_gtarski4(A, C, B)=k1_gtarski4(A, B, D) & k1_gtarski4(A, C, B)=k1_gtarski4(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(commutativity_k1_gtarski4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k1_gtarski4(A, B, C)=k1_gtarski4(A, C, B)) ) ).
fof(dt_k1_gtarski4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_gtarski4(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_gtarski3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_gtarski1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_gtarski3(A, B, C), k1_zfmisc_1(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(redefinition_k1_gtarski4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k1_gtarski4(A, B, C)=k2_gtarski3(A, B, C)) ) ).
fof(t39_gtarski1, 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)) =>  (r7_gtarski1(A, B, C, D) =>  (B=C |  (B=D | r8_gtarski1(A, B, C, B, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_gtarski3, axiom,  (! [A] :  ( (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_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)) =>  (r6_gtarski1(A, B, C, D) =>  (r6_gtarski1(A, C, D, B) &  (r6_gtarski1(A, D, B, C) &  (r6_gtarski1(A, D, C, B) &  (r6_gtarski1(A, C, B, D) & r6_gtarski1(A, B, D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t84_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)) =>  ( ( ~ (B=C)  & r6_gtarski1(A, B, C, D))  <=> r7_gtarski1(A, B, C, D)) ) ) ) ) ) ) ) ) ).
fof(t85_gtarski3, axiom,  (! [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)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r8_gtarski1(A, B, C, D, E) => k2_gtarski3(A, B, C)=k2_gtarski3(A, D, E)) ) ) ) ) ) ) ) ) ) ) ).
