% Mizar ND problem: t6_afvect0,afvect0,109,49 
fof(dh_c1_8__afvect0,definition,
    ( ( ( ~ v3_struct_0(c1_8__afvect0)
        & ~ v3_realset2(c1_8__afvect0)
        & v1_afvect0(c1_8__afvect0)
        & l1_analoaf(c1_8__afvect0) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(c1_8__afvect0))
                         => ( ( r2_analoaf(c1_8__afvect0,A,B,C,D)
                              & r2_analoaf(c1_8__afvect0,A,B,C,E) )
                           => D = E ) ) ) ) ) ) )
   => ! [F] : 
        ( ( ~ v3_struct_0(F)
          & ~ v3_realset2(F)
          & v1_afvect0(F)
          & l1_analoaf(F) )
       => ! [G] : 
            ( m1_subset_1(G,u1_struct_0(F))
           => ! [H] : 
                ( m1_subset_1(H,u1_struct_0(F))
               => ! [I] : 
                    ( m1_subset_1(I,u1_struct_0(F))
                   => ! [J] : 
                        ( m1_subset_1(J,u1_struct_0(F))
                       => ! [K] : 
                            ( m1_subset_1(K,u1_struct_0(F))
                           => ( ( r2_analoaf(F,G,H,I,J)
                                & r2_analoaf(F,G,H,I,K) )
                             => J = K ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_8__afvect0),file(afvect0,c1_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c1_8__afvect0)]).

fof(dh_c2_8__afvect0,definition,
    ( ( m1_subset_1(c2_8__afvect0,u1_struct_0(c1_8__afvect0))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
                     => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,A,B,C)
                          & r2_analoaf(c1_8__afvect0,c2_8__afvect0,A,B,D) )
                       => C = D ) ) ) ) ) )
   => ! [E] : 
        ( m1_subset_1(E,u1_struct_0(c1_8__afvect0))
       => ! [F] : 
            ( m1_subset_1(F,u1_struct_0(c1_8__afvect0))
           => ! [G] : 
                ( m1_subset_1(G,u1_struct_0(c1_8__afvect0))
               => ! [H] : 
                    ( m1_subset_1(H,u1_struct_0(c1_8__afvect0))
                   => ! [I] : 
                        ( m1_subset_1(I,u1_struct_0(c1_8__afvect0))
                       => ( ( r2_analoaf(c1_8__afvect0,E,F,G,H)
                            & r2_analoaf(c1_8__afvect0,E,F,G,I) )
                         => H = I ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_8__afvect0),file(afvect0,c2_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c2_8__afvect0)]).

fof(dh_c3_8__afvect0,definition,
    ( ( m1_subset_1(c3_8__afvect0,u1_struct_0(c1_8__afvect0))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
                 => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,A,B)
                      & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,A,C) )
                   => B = C ) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
       => ! [E] : 
            ( m1_subset_1(E,u1_struct_0(c1_8__afvect0))
           => ! [F] : 
                ( m1_subset_1(F,u1_struct_0(c1_8__afvect0))
               => ! [G] : 
                    ( m1_subset_1(G,u1_struct_0(c1_8__afvect0))
                   => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,D,E,F)
                        & r2_analoaf(c1_8__afvect0,c2_8__afvect0,D,E,G) )
                     => F = G ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_8__afvect0),file(afvect0,c3_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c3_8__afvect0)]).

fof(dh_c4_8__afvect0,definition,
    ( ( m1_subset_1(c4_8__afvect0,u1_struct_0(c1_8__afvect0))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
             => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A)
                  & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,B) )
               => A = B ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
           => ! [E] : 
                ( m1_subset_1(E,u1_struct_0(c1_8__afvect0))
               => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,C,D)
                    & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,C,E) )
                 => D = E ) ) ) ) ),
    introduced(definition,[new_symbol(c4_8__afvect0),file(afvect0,c4_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c4_8__afvect0)]).

fof(dh_c5_8__afvect0,definition,
    ( ( m1_subset_1(c5_8__afvect0,u1_struct_0(c1_8__afvect0))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
         => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
              & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A) )
           => c5_8__afvect0 = A ) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
           => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,B)
                & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,C) )
             => B = C ) ) ) ),
    introduced(definition,[new_symbol(c5_8__afvect0),file(afvect0,c5_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c5_8__afvect0)]).

fof(dh_c6_8__afvect0,definition,
    ( ( m1_subset_1(c6_8__afvect0,u1_struct_0(c1_8__afvect0))
     => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
          & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c6_8__afvect0) )
       => c5_8__afvect0 = c6_8__afvect0 ) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
       => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
            & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A) )
         => c5_8__afvect0 = A ) ) ),
    introduced(definition,[new_symbol(c6_8__afvect0),file(afvect0,c6_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c6_8__afvect0)]).

fof(e1_8__afvect0,assumption,
    ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
    & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c6_8__afvect0) ),
    introduced(assumption,[file(afvect0,e1_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,e1_8__afvect0)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    [interesting(0.9),axiom,file(analoaf,l1_analoaf)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    [interesting(0.9),axiom,file(analoaf,l1_analoaf)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_8__afvect0,assumption,
    ( ~ v3_struct_0(c1_8__afvect0)
    & ~ v3_realset2(c1_8__afvect0)
    & v1_afvect0(c1_8__afvect0)
    & l1_analoaf(c1_8__afvect0) ),
    introduced(assumption,[file(afvect0,c1_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c1_8__afvect0)]).

fof(dt_c4_8__afvect0,assumption,(
    m1_subset_1(c4_8__afvect0,u1_struct_0(c1_8__afvect0)) ),
    introduced(assumption,[file(afvect0,c4_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c4_8__afvect0)]).

fof(dt_c5_8__afvect0,assumption,(
    m1_subset_1(c5_8__afvect0,u1_struct_0(c1_8__afvect0)) ),
    introduced(assumption,[file(afvect0,c5_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c5_8__afvect0)]).

fof(dt_c6_8__afvect0,assumption,(
    m1_subset_1(c6_8__afvect0,u1_struct_0(c1_8__afvect0)) ),
    introduced(assumption,[file(afvect0,c6_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c6_8__afvect0)]).

fof(dt_c2_8__afvect0,assumption,(
    m1_subset_1(c2_8__afvect0,u1_struct_0(c1_8__afvect0)) ),
    introduced(assumption,[file(afvect0,c2_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c2_8__afvect0)]).

fof(dt_c3_8__afvect0,assumption,(
    m1_subset_1(c3_8__afvect0,u1_struct_0(c1_8__afvect0)) ),
    introduced(assumption,[file(afvect0,c3_8__afvect0)]),
    [interesting(0.8),axiom,file(afvect0,c3_8__afvect0)]).

fof(t4_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                       => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ),
    file(afvect0,t4_afvect0),
    [interesting(0.9),axiom,file(afvect0,t4_afvect0)]).

fof(e2_8__afvect0,plain,
    ( r2_analoaf(c1_8__afvect0,c4_8__afvect0,c5_8__afvect0,c2_8__afvect0,c3_8__afvect0)
    & r2_analoaf(c1_8__afvect0,c4_8__afvect0,c6_8__afvect0,c2_8__afvect0,c3_8__afvect0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e1_8__afvect0])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_l1_analoaf,existence_m1_subset_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e1_8__afvect0,t4_afvect0]),
    [interesting(0.8),file(afvect0,e2_8__afvect0),[file(afvect0,e2_8__afvect0)]]).

fof(d1_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_afvect0(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))
                     => ( r2_analoaf(A,B,C,D,D)
                       => B = C ) ) ) )
          & ! [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))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
          & ! [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))
                          & r2_analoaf(A,B,C,D,E) ) ) ) )
          & ! [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))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G) )
                                   => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
          & ! [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))
                      & r2_analoaf(A,B,D,D,C) ) ) )
          & ! [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))
                         => ( r2_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) ),
    file(afvect0,d1_afvect0),
    [interesting(0.9),axiom,file(afvect0,d1_afvect0)]).

fof(e3_8__afvect0,plain,(
    r2_analoaf(c1_8__afvect0,c4_8__afvect0,c5_8__afvect0,c4_8__afvect0,c6_8__afvect0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e1_8__afvect0])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_l1_analoaf,existence_m1_subset_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e2_8__afvect0,d1_afvect0]),
    [interesting(0.8),file(afvect0,e3_8__afvect0),[file(afvect0,e3_8__afvect0)]]).

fof(t5_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_analoaf(A,B,C,B,D)
                   => C = D ) ) ) ) ) ),
    file(afvect0,t5_afvect0),
    [interesting(0.9),axiom,file(afvect0,t5_afvect0)]).

fof(e4_8__afvect0,plain,(
    c5_8__afvect0 = c6_8__afvect0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e1_8__afvect0])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_l1_analoaf,existence_m1_subset_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e3_8__afvect0,t5_afvect0]),
    [interesting(0.8),file(afvect0,e4_8__afvect0),[file(afvect0,e4_8__afvect0)]]).

fof(i8_8__afvect0,theorem,(
    $true ),
    introduced(tautology,[file(afvect0,i8_8__afvect0)]),
    [interesting(0.8),trivial,file(afvect0,i8_8__afvect0)]).

fof(i7_8__afvect0,plain,(
    c5_8__afvect0 = c6_8__afvect0 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0,e1_8__afvect0])],[e4_8__afvect0,i8_8__afvect0]),
    [interesting(0.8),file(afvect0,i7_8__afvect0),[file(afvect0,i7_8__afvect0)]]).

fof(i6_8__afvect0,plain,
    ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
      & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c6_8__afvect0) )
   => c5_8__afvect0 = c6_8__afvect0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0,dt_c6_8__afvect0]),discharge_asm(discharge,[e1_8__afvect0])],[e1_8__afvect0,i7_8__afvect0]),
    [interesting(0.8),file(afvect0,i6_8__afvect0),[file(afvect0,i6_8__afvect0)]]).

fof(i6_8_tmp__afvect0,plain,
    ( m1_subset_1(c6_8__afvect0,u1_struct_0(c1_8__afvect0))
   => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
        & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c6_8__afvect0) )
     => c5_8__afvect0 = c6_8__afvect0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0]),discharge_asm(discharge,[dt_c6_8__afvect0])],[dt_c6_8__afvect0,i6_8__afvect0]),
    [interesting(0.8),i5_8__afvect0]).

fof(i5_8__afvect0,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
     => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
          & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A) )
       => c5_8__afvect0 = A ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0,dt_c5_8__afvect0])],[i6_8_tmp__afvect0,dh_c6_8__afvect0]),
    [interesting(0.8),file(afvect0,i5_8__afvect0),[file(afvect0,i5_8__afvect0)]]).

fof(i5_8_tmp__afvect0,plain,
    ( m1_subset_1(c5_8__afvect0,u1_struct_0(c1_8__afvect0))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
       => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,c5_8__afvect0)
            & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A) )
         => c5_8__afvect0 = A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0]),discharge_asm(discharge,[dt_c5_8__afvect0])],[dt_c5_8__afvect0,i5_8__afvect0]),
    [interesting(0.8),i4_8__afvect0]).

fof(i4_8__afvect0,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
         => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A)
              & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,B) )
           => A = B ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0,dt_c4_8__afvect0])],[i5_8_tmp__afvect0,dh_c5_8__afvect0]),
    [interesting(0.8),file(afvect0,i4_8__afvect0),[file(afvect0,i4_8__afvect0)]]).

fof(i4_8_tmp__afvect0,plain,
    ( m1_subset_1(c4_8__afvect0,u1_struct_0(c1_8__afvect0))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
           => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,A)
                & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,c4_8__afvect0,B) )
             => A = B ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0]),discharge_asm(discharge,[dt_c4_8__afvect0])],[dt_c4_8__afvect0,i4_8__afvect0]),
    [interesting(0.8),i3_8__afvect0]).

fof(i3_8__afvect0,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
             => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,A,B)
                  & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,A,C) )
               => B = C ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0,dt_c3_8__afvect0])],[i4_8_tmp__afvect0,dh_c4_8__afvect0]),
    [interesting(0.8),file(afvect0,i3_8__afvect0),[file(afvect0,i3_8__afvect0)]]).

fof(i3_8_tmp__afvect0,plain,
    ( m1_subset_1(c3_8__afvect0,u1_struct_0(c1_8__afvect0))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
               => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,A,B)
                    & r2_analoaf(c1_8__afvect0,c2_8__afvect0,c3_8__afvect0,A,C) )
                 => B = C ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0]),discharge_asm(discharge,[dt_c3_8__afvect0])],[dt_c3_8__afvect0,i3_8__afvect0]),
    [interesting(0.8),i2_8__afvect0]).

fof(i2_8__afvect0,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
                 => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,A,B,C)
                      & r2_analoaf(c1_8__afvect0,c2_8__afvect0,A,B,D) )
                   => C = D ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__afvect0,dt_c2_8__afvect0])],[i3_8_tmp__afvect0,dh_c3_8__afvect0]),
    [interesting(0.8),file(afvect0,i2_8__afvect0),[file(afvect0,i2_8__afvect0)]]).

fof(i2_8_tmp__afvect0,plain,
    ( m1_subset_1(c2_8__afvect0,u1_struct_0(c1_8__afvect0))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
                   => ( ( r2_analoaf(c1_8__afvect0,c2_8__afvect0,A,B,C)
                        & r2_analoaf(c1_8__afvect0,c2_8__afvect0,A,B,D) )
                     => C = D ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__afvect0]),discharge_asm(discharge,[dt_c2_8__afvect0])],[dt_c2_8__afvect0,i2_8__afvect0]),
    [interesting(0.8),i1_8__afvect0]).

fof(i1_8__afvect0,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(c1_8__afvect0))
                     => ( ( r2_analoaf(c1_8__afvect0,A,B,C,D)
                          & r2_analoaf(c1_8__afvect0,A,B,C,E) )
                       => D = E ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__afvect0])],[i2_8_tmp__afvect0,dh_c2_8__afvect0]),
    [interesting(0.8),file(afvect0,i1_8__afvect0),[file(afvect0,i1_8__afvect0)]]).

fof(i1_8_tmp__afvect0,plain,
    ( ( ~ v3_struct_0(c1_8__afvect0)
      & ~ v3_realset2(c1_8__afvect0)
      & v1_afvect0(c1_8__afvect0)
      & l1_analoaf(c1_8__afvect0) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__afvect0))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_8__afvect0))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_8__afvect0))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(c1_8__afvect0))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(c1_8__afvect0))
                       => ( ( r2_analoaf(c1_8__afvect0,A,B,C,D)
                            & r2_analoaf(c1_8__afvect0,A,B,C,E) )
                         => D = E ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__afvect0])],[dt_c1_8__afvect0,i1_8__afvect0]),
    [interesting(1),t6_afvect0]).

fof(t6_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                         => ( ( r2_analoaf(A,B,C,D,E)
                              & r2_analoaf(A,B,C,D,F) )
                           => E = F ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__afvect0,dh_c1_8__afvect0]),
    [interesting(1),file(afvect0,t6_afvect0),[file(afvect0,t6_afvect0)]]).