% Mizar problem: t22_euclmetr,euclmetr,696,53 
fof(t22_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,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))
                                 => ( ( r5_analmetr(A,B,C,B,D)
                                      & r5_analmetr(A,B,E,B,F)
                                      & r5_analmetr(A,B,G,B,H)
                                      & r5_analmetr(A,C,E,D,F)
                                      & r5_analmetr(A,C,G,D,H)
                                      & B = D )
                                   => ( r4_analmetr(A,B,G,B,C)
                                      | r4_analmetr(A,B,C,B,E)
                                      | r5_analmetr(A,E,G,F,H) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_analmetr,d11_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,t4_euclmetr,t80_analmetr,t81_analmetr,t85_analmetr]),
    [file(euclmetr,t22_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(d11_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,u1_struct_0(A))
                 => ( r6_analmetr(A,B,C,D)
                  <=> r4_analmetr(A,B,C,B,D) ) ) ) ) ) ),
    file(analmetr,d11_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(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(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(t81_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))
                     => ( r4_analmetr(A,B,C,D,E)
                       => ( r4_analmetr(A,B,C,E,D)
                          & r4_analmetr(A,C,B,D,E)
                          & r4_analmetr(A,C,B,E,D)
                          & r4_analmetr(A,D,E,B,C)
                          & r4_analmetr(A,D,E,C,B)
                          & r4_analmetr(A,E,D,B,C)
                          & r4_analmetr(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(analmetr,t81_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),
    []).