% Mizar problem: t6_jgraph_1,jgraph_1,116,45 
fof(t6_jgraph_1,conjecture,(
    ! [A] : u1_graph_1(k1_jgraph_1(A)) = A ),
    inference(mizar_bg_added,[status(thm)],[reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u2_graph_1,dt_u3_graph_1,dt_u4_graph_1,cc1_relset_1,t3_subset,abstractness_v1_graph_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k7_funct_3,dt_k8_funct_3,dt_m1_relset_1,dt_m2_relset_1,free_g1_graph_1,existence_l1_graph_1,redefinition_k10_funct_3,redefinition_k9_funct_3,dt_g1_graph_1,dt_k10_funct_3,dt_k2_zfmisc_1,dt_k9_funct_3,dt_l1_graph_1,dt_k1_jgraph_1,dt_u1_graph_1,d1_jgraph_1]),
    [file(jgraph_1,t6_jgraph_1)]).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u2_graph_1,axiom,(
    $true ),
    file(graph_1,u2_graph_1),
    []).

fof(dt_u3_graph_1,axiom,(
    ! [A] : 
      ( l1_graph_1(A)
     => ( v1_funct_1(u3_graph_1(A))
        & v1_funct_2(u3_graph_1(A),u2_graph_1(A),u1_graph_1(A))
        & m2_relset_1(u3_graph_1(A),u2_graph_1(A),u1_graph_1(A)) ) ) ),
    file(graph_1,u3_graph_1),
    []).

fof(dt_u4_graph_1,axiom,(
    ! [A] : 
      ( l1_graph_1(A)
     => ( v1_funct_1(u4_graph_1(A))
        & v1_funct_2(u4_graph_1(A),u2_graph_1(A),u1_graph_1(A))
        & m2_relset_1(u4_graph_1(A),u2_graph_1(A),u1_graph_1(A)) ) ) ),
    file(graph_1,u4_graph_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(abstractness_v1_graph_1,axiom,(
    ! [A] : 
      ( l1_graph_1(A)
     => ( v1_graph_1(A)
       => A = g1_graph_1(u1_graph_1(A),u2_graph_1(A),u3_graph_1(A),u4_graph_1(A)) ) ) ),
    file(graph_1,v1_graph_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_k7_funct_3,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k7_funct_3(A,B))
      & v1_funct_1(k7_funct_3(A,B)) ) ),
    file(funct_3,k7_funct_3),
    []).

fof(dt_k8_funct_3,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k8_funct_3(A,B))
      & v1_funct_1(k8_funct_3(A,B)) ) ),
    file(funct_3,k8_funct_3),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(free_g1_graph_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ! [E,F,G,H] : 
          ( g1_graph_1(A,B,C,D) = g1_graph_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(graph_1,g1_graph_1),
    []).

fof(existence_l1_graph_1,axiom,(
    ? [A] : l1_graph_1(A) ),
    file(graph_1,l1_graph_1),
    []).

fof(redefinition_k10_funct_3,axiom,(
    ! [A,B] : k10_funct_3(A,B) = k8_funct_3(A,B) ),
    file(funct_3,k10_funct_3),
    []).

fof(redefinition_k9_funct_3,axiom,(
    ! [A,B] : k9_funct_3(A,B) = k7_funct_3(A,B) ),
    file(funct_3,k9_funct_3),
    []).

fof(dt_g1_graph_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( v1_graph_1(g1_graph_1(A,B,C,D))
        & l1_graph_1(g1_graph_1(A,B,C,D)) ) ) ),
    file(graph_1,g1_graph_1),
    []).

fof(dt_k10_funct_3,axiom,(
    ! [A,B] : 
      ( v1_funct_1(k10_funct_3(A,B))
      & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B)
      & m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) ) ),
    file(funct_3,k10_funct_3),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k9_funct_3,axiom,(
    ! [A,B] : 
      ( v1_funct_1(k9_funct_3(A,B))
      & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A)
      & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) ) ),
    file(funct_3,k9_funct_3),
    []).

fof(dt_l1_graph_1,axiom,(
    $true ),
    file(graph_1,l1_graph_1),
    []).

fof(dt_k1_jgraph_1,axiom,(
    ! [A] : l1_graph_1(k1_jgraph_1(A)) ),
    file(jgraph_1,k1_jgraph_1),
    []).

fof(dt_u1_graph_1,axiom,(
    $true ),
    file(graph_1,u1_graph_1),
    []).

fof(d1_jgraph_1,axiom,(
    ! [A] : k1_jgraph_1(A) = g1_graph_1(A,k2_zfmisc_1(A,A),k9_funct_3(A,A),k10_funct_3(A,A)) ),
    file(jgraph_1,d1_jgraph_1),
    []).