% Mizar problem: t6_jgraph_5,jgraph_5,152,5 
fof(t6_jgraph_5, conjecture,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (l1_pre_topc(B) =>  (! [C] :  (l1_pre_topc(C) =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  =>  ( (v3_tops_2(E, B, C) & v2_funct_1(D))  => v2_funct_1(k1_partfun1(u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_struct_0(C), D, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(d3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k2_struct_0(A)=u1_struct_0(A)) ) ).
fof(d5_tops_2, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (l1_pre_topc(B) =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v3_tops_2(C, A, B) <=>  (k1_relset_1(u1_struct_0(A), C)=k2_struct_0(A) &  (k2_relset_1(u1_struct_0(B), C)=k2_struct_0(B) &  (v2_funct_1(C) &  (v5_pre_topc(C, A, B) & v5_pre_topc(k2_tops_2(u1_struct_0(A), u1_struct_0(B), C), B, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_partfun1, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) )  =>  (v1_funct_1(k1_partfun1(A, B, C, D, E, F)) & m1_subset_1(k1_partfun1(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(A, D)))) ) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k2_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_tops_2, axiom,  (! [A, B, C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (v1_funct_1(k2_tops_2(A, B, C)) &  (v1_funct_2(k2_tops_2(A, B, C), B, A) & m1_subset_1(k2_tops_2(A, B, C), k1_zfmisc_1(k2_zfmisc_1(B, A)))) ) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(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_pre_topc, axiom,  (? [A] : l1_pre_topc(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(fc12_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ~ (v1_subset_1(k2_struct_0(A), u1_struct_0(A))) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc4_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc5_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(redefinition_k1_partfun1, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) )  => k1_partfun1(A, B, C, D, E, F)=k3_relat_1(E, F)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
