% Mizar ND problem: t10_aff_1,aff_1,30,19 
fof(dh_c1_2__aff_1,definition,
    ( ( ( ~ v3_struct_0(c1_2__aff_1)
        & ~ v3_realset2(c1_2__aff_1)
        & v1_diraf(c1_2__aff_1)
        & l1_analoaf(c1_2__aff_1) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
         => ~ ! [B] : 
                ( m1_subset_1(B,u1_struct_0(c1_2__aff_1))
               => A = B ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & ~ v3_realset2(C)
          & v1_diraf(C)
          & l1_analoaf(C) )
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(C))
           => ~ ! [E] : 
                  ( m1_subset_1(E,u1_struct_0(C))
                 => D = E ) ) ) ),
    introduced(definition,[new_symbol(c1_2__aff_1),file(aff_1,c1_2__aff_1)]),
    [interesting(0.8),axiom,file(aff_1,c1_2__aff_1)]).

fof(dh_c2_2__aff_1,definition,
    ( ( m1_subset_1(c2_2__aff_1,u1_struct_0(c1_2__aff_1))
     => ~ ! [A] : 
            ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
           => c2_2__aff_1 = A ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_2__aff_1))
       => ~ ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_2__aff_1))
             => B = C ) ) ),
    introduced(definition,[new_symbol(c2_2__aff_1),file(aff_1,c2_2__aff_1)]),
    [interesting(0.8),axiom,file(aff_1,c2_2__aff_1)]).

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

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

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_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_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_2__aff_1,assumption,
    ( ~ v3_struct_0(c1_2__aff_1)
    & ~ v3_realset2(c1_2__aff_1)
    & v1_diraf(c1_2__aff_1)
    & l1_analoaf(c1_2__aff_1) ),
    introduced(assumption,[file(aff_1,c1_2__aff_1)]),
    [interesting(0.8),axiom,file(aff_1,c1_2__aff_1)]).

fof(dt_c2_2__aff_1,assumption,(
    m1_subset_1(c2_2__aff_1,u1_struct_0(c1_2__aff_1)) ),
    introduced(assumption,[file(aff_1,c2_2__aff_1)]),
    [interesting(0.8),axiom,file(aff_1,c2_2__aff_1)]).

fof(dh_c3_2__aff_1,definition,
    ( ~ ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_2__aff_1))
             => A = B ) )
   => ( m1_subset_1(c3_2__aff_1,u1_struct_0(c1_2__aff_1))
      & ~ ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c1_2__aff_1))
           => c3_2__aff_1 = C ) ) ),
    introduced(definition,[new_symbol(c3_2__aff_1),file(aff_1,c3_2__aff_1)]),
    [interesting(0.8),axiom,file(aff_1,c3_2__aff_1)]).

fof(t47_diraf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => 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,C,B)
                                  & r2_analoaf(A,B,C,D,D)
                                  & ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,B,C,F,G) )
                                   => ( B = C
                                      | r2_analoaf(A,D,E,F,G) ) )
                                  & ( r2_analoaf(A,B,C,B,D)
                                   => r2_analoaf(A,C,B,C,D) ) ) ) ) ) ) ) )
        & ~ ! [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) ) ) )
        & ! [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,D,C,E)
                        & C != 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)
                        & r2_analoaf(A,B,D,C,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,D,B,B,E)
                            & B != D
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_analoaf(A,C,B,B,F)
                                    & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ),
    file(diraf,t47_diraf),
    [interesting(0.9),axiom,file(diraf,t47_diraf)]).

fof(e1_2__aff_1,plain,(
    ~ ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_2__aff_1))
           => A = B ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__aff_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,t1_subset,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_2__aff_1,t47_diraf]),
    [interesting(0.8),file(aff_1,e1_2__aff_1),[file(aff_1,e1_2__aff_1)]]).

fof(dt_c3_2__aff_1,plain,(
    m1_subset_1(c3_2__aff_1,u1_struct_0(c1_2__aff_1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__aff_1])],[dh_c3_2__aff_1,e1_2__aff_1]),
    [interesting(0.8),file(aff_1,c3_2__aff_1),[file(aff_1,c3_2__aff_1)]]).

fof(dh_c4_2__aff_1,definition,
    ( ~ ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
         => c3_2__aff_1 = A )
   => ( m1_subset_1(c4_2__aff_1,u1_struct_0(c1_2__aff_1))
      & c3_2__aff_1 != c4_2__aff_1 ) ),
    introduced(definition,[new_symbol(c4_2__aff_1),file(aff_1,c4_2__aff_1)]),
    [interesting(0.8),axiom,file(aff_1,c4_2__aff_1)]).

fof(dt_c4_2__aff_1,plain,(
    m1_subset_1(c4_2__aff_1,u1_struct_0(c1_2__aff_1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__aff_1])],[dh_c3_2__aff_1,dh_c4_2__aff_1,e1_2__aff_1]),
    [interesting(0.8),file(aff_1,c4_2__aff_1),[file(aff_1,c4_2__aff_1)]]).

fof(e2_2__aff_1,plain,(
    c3_2__aff_1 != c4_2__aff_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_2__aff_1])],[dh_c3_2__aff_1,dh_c4_2__aff_1,e1_2__aff_1]),
    [interesting(0.8),file(aff_1,e2_2__aff_1),[file(aff_1,e2_2__aff_1)]]).

fof(e3_2__aff_1,plain,(
    ~ ( c2_2__aff_1 = c3_2__aff_1
      & c2_2__aff_1 = c4_2__aff_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__aff_1,dt_c1_2__aff_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_analoaf,existence_l1_struct_0,dt_l1_analoaf,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__aff_1,dt_c2_2__aff_1,dt_c3_2__aff_1,dt_c4_2__aff_1,e2_2__aff_1]),
    [interesting(0.8),file(aff_1,e3_2__aff_1),[file(aff_1,e3_2__aff_1)]]).

fof(e4_2__aff_1,plain,(
    ~ ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
       => c2_2__aff_1 = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__aff_1,dt_c1_2__aff_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_analoaf,existence_l1_struct_0,dt_l1_analoaf,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__aff_1,dt_c2_2__aff_1,dt_c3_2__aff_1,dt_c4_2__aff_1,e3_2__aff_1]),
    [interesting(0.8),file(aff_1,e4_2__aff_1),[file(aff_1,e4_2__aff_1)]]).

fof(i3_2__aff_1,theorem,(
    $true ),
    introduced(tautology,[file(aff_1,i3_2__aff_1)]),
    [interesting(0.8),trivial,file(aff_1,i3_2__aff_1)]).

fof(i2_2__aff_1,plain,(
    ~ ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
       => c2_2__aff_1 = A ) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_2__aff_1,dt_c1_2__aff_1])],[e4_2__aff_1,i3_2__aff_1]),
    [interesting(0.8),file(aff_1,i2_2__aff_1),[file(aff_1,i2_2__aff_1)]]).

fof(i2_2_tmp__aff_1,plain,
    ( m1_subset_1(c2_2__aff_1,u1_struct_0(c1_2__aff_1))
   => ~ ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
         => c2_2__aff_1 = A ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__aff_1]),discharge_asm(discharge,[dt_c2_2__aff_1])],[dt_c2_2__aff_1,i2_2__aff_1]),
    [interesting(0.8),i1_2__aff_1]).

fof(i1_2__aff_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
     => ~ ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_2__aff_1))
           => A = B ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__aff_1])],[i2_2_tmp__aff_1,dh_c2_2__aff_1]),
    [interesting(0.8),file(aff_1,i1_2__aff_1),[file(aff_1,i1_2__aff_1)]]).

fof(i1_2_tmp__aff_1,plain,
    ( ( ~ v3_struct_0(c1_2__aff_1)
      & ~ v3_realset2(c1_2__aff_1)
      & v1_diraf(c1_2__aff_1)
      & l1_analoaf(c1_2__aff_1) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__aff_1))
       => ~ ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_2__aff_1))
             => A = B ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__aff_1])],[dt_c1_2__aff_1,i1_2__aff_1]),
    [interesting(1),t10_aff_1]).

fof(t10_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__aff_1,dh_c1_2__aff_1]),
    [interesting(1),file(aff_1,t10_aff_1),[file(aff_1,t10_aff_1)]]).