% Mizar problem: t1_conmetr1,conmetr1,98,73 
fof(t1_conmetr1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_conmetr1(A)
      <=> ( v5_conmetr1(A)
          & v6_conmetr1(A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d4_conmetr1,d5_conmetr1,d6_conmetr1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_analoaf,existence_l1_struct_0,existence_m1_subset_1,redefinition_r4_aff_1,reflexivity_r1_tarski,symmetry_r4_aff_1,t1_subset,t3_subset,t4_subset,t50_aff_1,t72_aff_1]),
    [file(conmetr1,t1_conmetr1)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(d4_conmetr1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_conmetr1(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))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                           => ! [K] : 
                                                ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                               => ( ( v1_aff_1(J,A)
                                                    & v1_aff_1(K,A)
                                                    & r2_hidden(B,J)
                                                    & r2_hidden(D,J)
                                                    & r2_hidden(G,J)
                                                    & r2_hidden(I,J)
                                                    & r2_hidden(C,K)
                                                    & r2_hidden(E,K)
                                                    & r2_hidden(F,K)
                                                    & r2_hidden(H,K)
                                                    & r2_analoaf(A,D,C,H,G)
                                                    & r2_analoaf(A,C,B,G,F)
                                                    & r2_analoaf(A,B,E,F,I) )
                                                 => ( r2_hidden(E,J)
                                                    | r2_hidden(C,J)
                                                    | r2_hidden(F,J)
                                                    | r2_hidden(H,J)
                                                    | r2_hidden(B,K)
                                                    | r2_hidden(D,K)
                                                    | r2_hidden(G,K)
                                                    | r2_hidden(I,K)
                                                    | r2_analoaf(A,D,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(conmetr1,d4_conmetr1),
    []).

fof(d5_conmetr1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v5_conmetr1(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))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                           => ! [K] : 
                                                ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                               => ( ( r4_aff_1(A,J,K)
                                                    & r2_hidden(B,J)
                                                    & r2_hidden(D,J)
                                                    & r2_hidden(G,J)
                                                    & r2_hidden(I,J)
                                                    & r2_hidden(C,K)
                                                    & r2_hidden(E,K)
                                                    & r2_hidden(F,K)
                                                    & r2_hidden(H,K)
                                                    & r2_analoaf(A,D,C,H,G)
                                                    & r2_analoaf(A,C,B,G,F)
                                                    & r2_analoaf(A,B,E,F,I) )
                                                 => ( r2_hidden(E,J)
                                                    | r2_hidden(C,J)
                                                    | r2_hidden(F,J)
                                                    | r2_hidden(H,J)
                                                    | r2_hidden(B,K)
                                                    | r2_hidden(D,K)
                                                    | r2_hidden(G,K)
                                                    | r2_hidden(I,K)
                                                    | r2_analoaf(A,D,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(conmetr1,d5_conmetr1),
    []).

fof(d6_conmetr1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v6_conmetr1(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))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                               => ! [L] : 
                                                    ( m1_subset_1(L,k1_zfmisc_1(u1_struct_0(A)))
                                                   => ( ( v1_aff_1(K,A)
                                                        & v1_aff_1(L,A)
                                                        & r2_hidden(B,K)
                                                        & r2_hidden(B,L)
                                                        & r2_hidden(C,K)
                                                        & r2_hidden(E,K)
                                                        & r2_hidden(H,K)
                                                        & r2_hidden(J,K)
                                                        & r2_hidden(D,L)
                                                        & r2_hidden(F,L)
                                                        & r2_hidden(G,L)
                                                        & r2_hidden(I,L)
                                                        & r2_analoaf(A,E,D,I,H)
                                                        & r2_analoaf(A,D,C,H,G)
                                                        & r2_analoaf(A,C,F,G,J) )
                                                     => ( r2_hidden(F,K)
                                                        | r2_hidden(D,K)
                                                        | r2_hidden(G,K)
                                                        | r2_hidden(I,K)
                                                        | r2_hidden(C,L)
                                                        | r2_hidden(E,L)
                                                        | r2_hidden(H,L)
                                                        | r2_hidden(J,L)
                                                        | r2_analoaf(A,E,F,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(conmetr1,d6_conmetr1),
    []).

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

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

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

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

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

fof(redefinition_r4_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_aff_1(A,B,C)
      <=> r3_aff_1(A,B,C) ) ) ),
    file(aff_1,r4_aff_1),
    []).

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

fof(symmetry_r4_aff_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r4_aff_1(A,B,C)
       => r4_aff_1(A,C,B) ) ) ),
    file(aff_1,r4_aff_1),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t50_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r3_aff_1(A,B,C)
               => ( v1_aff_1(B,A)
                  & v1_aff_1(C,A) ) ) ) ) ) ),
    file(aff_1,t50_aff_1),
    []).

fof(t72_aff_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(B,A)
                  & v1_aff_1(C,A)
                  & ~ r4_aff_1(A,B,C)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,B)
                          & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(aff_1,t72_aff_1),
    []).