% Mizar problem: t8_euclmetr,euclmetr,174,44 
fof(t8_euclmetr,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v1_euclmetr(A)
      <=> v3_conaffm(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_analmetr,d1_euclmetr,d3_conaffm,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,t4_euclmetr,t5_euclmetr,t6_euclmetr,t7_euclmetr,t80_analmetr,t83_analmetr]),
    [file(euclmetr,t8_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(d1_euclmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v1_euclmetr(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))
                       => ( ( r5_analmetr(A,B,C,D,E)
                            & r5_analmetr(A,C,D,B,E) )
                         => r5_analmetr(A,C,E,B,D) ) ) ) ) ) ) ) ),
    file(euclmetr,d1_euclmetr),
    []).

fof(d3_conaffm,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v3_conaffm(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_analmetr(A,B,C,D)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r5_analmetr(A,E,B,C,D)
                                & r5_analmetr(A,E,C,B,D)
                                & r5_analmetr(A,E,D,B,C) ) ) ) ) ) ) ) ) ),
    file(conaffm,d3_conaffm),
    []).

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(t4_euclmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_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))
                 => ( r6_analmetr(A,B,C,D)
                   => ( r6_analmetr(A,B,D,C)
                      & r6_analmetr(A,C,B,D)
                      & r6_analmetr(A,C,D,B)
                      & r6_analmetr(A,D,B,C)
                      & r6_analmetr(A,D,C,B) ) ) ) ) ) ) ),
    file(euclmetr,t4_euclmetr),
    []).

fof(t5_euclmetr,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))
                 => ~ ( ~ r6_analmetr(A,B,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r5_analmetr(A,E,B,C,D)
                              & r5_analmetr(A,E,C,B,D) ) ) ) ) ) ) ) ),
    file(euclmetr,t5_euclmetr),
    []).

fof(t6_euclmetr,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))
                         => ( ( r5_analmetr(A,E,B,C,D)
                              & r5_analmetr(A,E,C,B,D)
                              & r5_analmetr(A,F,B,C,D)
                              & r5_analmetr(A,F,C,B,D) )
                           => ( r6_analmetr(A,B,C,D)
                              | E = F ) ) ) ) ) ) ) ) ),
    file(euclmetr,t6_euclmetr),
    []).

fof(t7_euclmetr,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))
                     => ~ ( r5_analmetr(A,B,C,D,E)
                          & r5_analmetr(A,C,D,B,E)
                          & r6_analmetr(A,B,C,D)
                          & B != D
                          & B != C
                          & C != D ) ) ) ) ) ) ),
    file(euclmetr,t7_euclmetr),
    []).

fof(t80_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_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))
                 => ( r5_analmetr(A,B,C,D,D)
                    & r5_analmetr(A,D,D,B,C)
                    & r4_analmetr(A,B,C,D,D)
                    & r4_analmetr(A,D,D,B,C) ) ) ) ) ) ),
    file(analmetr,t80_analmetr),
    []).

fof(t83_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_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))
                     => ( r5_analmetr(A,B,C,D,E)
                       => ( r5_analmetr(A,B,C,E,D)
                          & r5_analmetr(A,C,B,D,E)
                          & r5_analmetr(A,C,B,E,D)
                          & r5_analmetr(A,D,E,B,C)
                          & r5_analmetr(A,D,E,C,B)
                          & r5_analmetr(A,E,D,B,C)
                          & r5_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(analmetr,t83_analmetr),
    []).