% Mizar problem: t3_euclmetr,euclmetr,79,11 
fof(t3_euclmetr,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( B != C
                          & ( r7_analmetr(A,B,C,E)
                            | r7_analmetr(A,C,B,E) )
                          & ( r7_analmetr(A,B,C,D)
                            | r7_analmetr(A,C,B,D) )
                          & ~ r10_analmetr(A,E,D) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_analmetr,d14_analmetr,d16_analmetr,dt_k1_zfmisc_1,dt_k4_analmetr,dt_l1_analmetr,dt_l1_analoaf,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_analmetr,existence_l1_analoaf,existence_l1_struct_0,existence_m1_subset_1,rc2_analmetr,redefinition_r10_analmetr,reflexivity_r1_tarski,symmetry_r10_analmetr,t3_subset,t67_analmetr,t85_analmetr]),
    [file(euclmetr,t3_euclmetr)]).

fof(cc1_analmetr,axiom,(
    ! [A] : 
      ( l1_analmetr(A)
     => ( ( ~ v3_struct_0(A)
          & v3_analmetr(A) )
       => ( ~ v3_struct_0(A)
          & v2_analmetr(A) ) ) ) ),
    file(analmetr,cc1_analmetr),
    []).

fof(d14_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r7_analmetr(A,B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & ? [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                            & E != F
                            & D = k4_analmetr(A,E,F)
                            & r5_analmetr(A,B,C,E,F) ) ) ) ) ) ) ) ),
    file(analmetr,d14_analmetr),
    []).

fof(d16_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(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)))
             => ( r9_analmetr(A,B,C)
              <=> ? [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))
                                & D != E
                                & F != G
                                & B = k4_analmetr(A,D,E)
                                & C = k4_analmetr(A,F,G)
                                & r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ),
    file(analmetr,d16_analmetr),
    []).

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

fof(dt_k4_analmetr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_analmetr(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(analmetr,k4_analmetr),
    []).

fof(dt_l1_analmetr,axiom,(
    ! [A] : 
      ( l1_analmetr(A)
     => l1_analoaf(A) ) ),
    file(analmetr,l1_analmetr),
    []).

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_analmetr,axiom,(
    ? [A] : l1_analmetr(A) ),
    file(analmetr,l1_analmetr),
    []).

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(rc2_analmetr,axiom,(
    ? [A] : 
      ( l1_analmetr(A)
      & ~ v3_struct_0(A) ) ),
    file(analmetr,rc2_analmetr),
    []).

fof(redefinition_r10_analmetr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r10_analmetr(A,B,C)
      <=> r9_analmetr(A,B,C) ) ) ),
    file(analmetr,r10_analmetr),
    []).

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

fof(symmetry_r10_analmetr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( r10_analmetr(A,B,C)
       => r10_analmetr(A,C,B) ) ) ),
    file(analmetr,r10_analmetr),
    []).

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

fof(t67_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r7_analmetr(A,C,D,B)
                   => r7_analmetr(A,D,C,B) ) ) ) ) ) ),
    file(analmetr,t67_analmetr),
    []).

fof(t85_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                             => ~ ( B != C
                                  & ~ ( ~ ( r5_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,B,C,F,G) )
                                      & ~ ( r5_analmetr(A,B,C,D,E)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r5_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,F,G,B,C) )
                                      & ~ ( r5_analmetr(A,D,E,B,C)
                                          & r5_analmetr(A,B,C,F,G) ) )
                                  & ~ r4_analmetr(A,D,E,F,G) ) ) ) ) ) ) ) ) ),
    file(analmetr,t85_analmetr),
    []).