% Mizar ND problem: t6_funct_3,funct_3,160,13 
fof(dh_c1_8__funct_3,definition,
    ( ! [A,B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( k1_relat_1(B) = k2_zfmisc_1(c1_8__funct_3,A)
                & k1_relat_1(C) = k2_zfmisc_1(c1_8__funct_3,A)
                & ! [D,E] : 
                    ( ( r2_hidden(D,c1_8__funct_3)
                      & r2_hidden(E,A) )
                   => k1_funct_1(B,k4_tarski(D,E)) = k1_funct_1(C,k4_tarski(D,E)) ) )
             => B = C ) ) )
   => ! [F,G,H] : 
        ( ( v1_relat_1(H)
          & v1_funct_1(H) )
       => ! [I] : 
            ( ( v1_relat_1(I)
              & v1_funct_1(I) )
           => ( ( k1_relat_1(H) = k2_zfmisc_1(F,G)
                & k1_relat_1(I) = k2_zfmisc_1(F,G)
                & ! [J,K] : 
                    ( ( r2_hidden(J,F)
                      & r2_hidden(K,G) )
                   => k1_funct_1(H,k4_tarski(J,K)) = k1_funct_1(I,k4_tarski(J,K)) ) )
             => H = I ) ) ) ),
    introduced(definition,[new_symbol(c1_8__funct_3),file(funct_3,c1_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c1_8__funct_3)]).

fof(dh_c2_8__funct_3,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( ( k1_relat_1(A) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
                & k1_relat_1(B) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
                & ! [C,D] : 
                    ( ( r2_hidden(C,c1_8__funct_3)
                      & r2_hidden(D,c2_8__funct_3) )
                   => k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(C,D)) ) )
             => A = B ) ) )
   => ! [E,F] : 
        ( ( v1_relat_1(F)
          & v1_funct_1(F) )
       => ! [G] : 
            ( ( v1_relat_1(G)
              & v1_funct_1(G) )
           => ( ( k1_relat_1(F) = k2_zfmisc_1(c1_8__funct_3,E)
                & k1_relat_1(G) = k2_zfmisc_1(c1_8__funct_3,E)
                & ! [H,I] : 
                    ( ( r2_hidden(H,c1_8__funct_3)
                      & r2_hidden(I,E) )
                   => k1_funct_1(F,k4_tarski(H,I)) = k1_funct_1(G,k4_tarski(H,I)) ) )
             => F = G ) ) ) ),
    introduced(definition,[new_symbol(c2_8__funct_3),file(funct_3,c2_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c2_8__funct_3)]).

fof(dh_c3_8__funct_3,definition,
    ( ( ( v1_relat_1(c3_8__funct_3)
        & v1_funct_1(c3_8__funct_3) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( k1_relat_1(c3_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
              & k1_relat_1(A) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
              & ! [B,C] : 
                  ( ( r2_hidden(B,c1_8__funct_3)
                    & r2_hidden(C,c2_8__funct_3) )
                 => k1_funct_1(c3_8__funct_3,k4_tarski(B,C)) = k1_funct_1(A,k4_tarski(B,C)) ) )
           => c3_8__funct_3 = A ) ) )
   => ! [D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D) )
       => ! [E] : 
            ( ( v1_relat_1(E)
              & v1_funct_1(E) )
           => ( ( k1_relat_1(D) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
                & k1_relat_1(E) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
                & ! [F,G] : 
                    ( ( r2_hidden(F,c1_8__funct_3)
                      & r2_hidden(G,c2_8__funct_3) )
                   => k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) ) )
             => D = E ) ) ) ),
    introduced(definition,[new_symbol(c3_8__funct_3),file(funct_3,c3_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c3_8__funct_3)]).

fof(dh_c4_8__funct_3,definition,
    ( ( ( v1_relat_1(c4_8__funct_3)
        & v1_funct_1(c4_8__funct_3) )
     => ( ( k1_relat_1(c3_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
          & k1_relat_1(c4_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
          & ! [A,B] : 
              ( ( r2_hidden(A,c1_8__funct_3)
                & r2_hidden(B,c2_8__funct_3) )
             => k1_funct_1(c3_8__funct_3,k4_tarski(A,B)) = k1_funct_1(c4_8__funct_3,k4_tarski(A,B)) ) )
       => c3_8__funct_3 = c4_8__funct_3 ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ( ( k1_relat_1(c3_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
            & k1_relat_1(C) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
            & ! [D,E] : 
                ( ( r2_hidden(D,c1_8__funct_3)
                  & r2_hidden(E,c2_8__funct_3) )
               => k1_funct_1(c3_8__funct_3,k4_tarski(D,E)) = k1_funct_1(C,k4_tarski(D,E)) ) )
         => c3_8__funct_3 = C ) ) ),
    introduced(definition,[new_symbol(c4_8__funct_3),file(funct_3,c4_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c4_8__funct_3)]).

fof(e1_8__funct_3,assumption,
    ( k1_relat_1(c3_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
    & k1_relat_1(c4_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3) ),
    introduced(assumption,[file(funct_3,e1_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,e1_8__funct_3)]).

fof(e2_8__funct_3,assumption,(
    ! [A,B] : 
      ( ( r2_hidden(A,c1_8__funct_3)
        & r2_hidden(B,c2_8__funct_3) )
     => k1_funct_1(c3_8__funct_3,k4_tarski(A,B)) = k1_funct_1(c4_8__funct_3,k4_tarski(A,B)) ) ),
    introduced(assumption,[file(funct_3,e2_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,e2_8__funct_3)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

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

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

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(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

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(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

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_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

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(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(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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_c1_8__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c1_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c1_8__funct_3)]).

fof(dt_c2_8__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c2_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c2_8__funct_3)]).

fof(dt_c3_8__funct_3,assumption,
    ( v1_relat_1(c3_8__funct_3)
    & v1_funct_1(c3_8__funct_3) ),
    introduced(assumption,[file(funct_3,c3_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c3_8__funct_3)]).

fof(dt_c4_8__funct_3,assumption,
    ( v1_relat_1(c4_8__funct_3)
    & v1_funct_1(c4_8__funct_3) ),
    introduced(assumption,[file(funct_3,c4_8__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c4_8__funct_3)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

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(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(dh_c1_8_1__funct_3,definition,
    ( ( r2_hidden(c1_8_1__funct_3,k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3))
     => k1_funct_1(c3_8__funct_3,c1_8_1__funct_3) = k1_funct_1(c4_8__funct_3,c1_8_1__funct_3) )
   => ! [A] : 
        ( r2_hidden(A,k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3))
       => k1_funct_1(c3_8__funct_3,A) = k1_funct_1(c4_8__funct_3,A) ) ),
    introduced(definition,[new_symbol(c1_8_1__funct_3),file(funct_3,c1_8_1__funct_3)]),
    [interesting(0.65),axiom,file(funct_3,c1_8_1__funct_3)]).

fof(e1_8_1__funct_3,assumption,(
    r2_hidden(c1_8_1__funct_3,k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)) ),
    introduced(assumption,[file(funct_3,e1_8_1__funct_3)]),
    [interesting(0.65),axiom,file(funct_3,e1_8_1__funct_3)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_c1_8_1__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c1_8_1__funct_3)]),
    [interesting(0.65),axiom,file(funct_3,c1_8_1__funct_3)]).

fof(fc1_zfmisc_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,fc1_zfmisc_1)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(d2_zfmisc_1,definition,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,d2_zfmisc_1)]).

fof(e2_8_1__funct_3,plain,(
    ? [A,B] : 
      ( r2_hidden(A,c1_8__funct_3)
      & r2_hidden(B,c2_8__funct_3)
      & c1_8_1__funct_3 = k4_tarski(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__funct_3,dt_c1_8_1__funct_3,dt_c2_8__funct_3,e1_8_1__funct_3])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_8__funct_3,dt_c1_8_1__funct_3,dt_c2_8__funct_3,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e1_8_1__funct_3,d2_zfmisc_1]),
    [interesting(0.65),file(funct_3,e2_8_1__funct_3),[file(funct_3,e2_8_1__funct_3)]]).

fof(e3_8_1__funct_3,plain,(
    k1_funct_1(c3_8__funct_3,c1_8_1__funct_3) = k1_funct_1(c4_8__funct_3,c1_8_1__funct_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c1_8_1__funct_3,dt_c2_8__funct_3,e1_8_1__funct_3,e2_8__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_subset_1,fc3_subset_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k4_tarski,dt_c1_8__funct_3,dt_c1_8_1__funct_3,dt_c2_8__funct_3,dt_c3_8__funct_3,dt_c4_8__funct_3,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e2_8_1__funct_3,e2_8__funct_3]),
    [interesting(0.65),file(funct_3,e3_8_1__funct_3),[file(funct_3,e3_8_1__funct_3)]]).

fof(i3_8_1__funct_3,theorem,(
    $true ),
    introduced(tautology,[file(funct_3,i3_8_1__funct_3)]),
    [interesting(0.65),trivial,file(funct_3,i3_8_1__funct_3)]).

fof(i2_8_1__funct_3,plain,(
    k1_funct_1(c3_8__funct_3,c1_8_1__funct_3) = k1_funct_1(c4_8__funct_3,c1_8_1__funct_3) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c1_8_1__funct_3,dt_c2_8__funct_3,e1_8_1__funct_3,e2_8__funct_3])],[e3_8_1__funct_3,i3_8_1__funct_3]),
    [interesting(0.65),file(funct_3,i2_8_1__funct_3),[file(funct_3,i2_8_1__funct_3)]]).

fof(i1_8_1__funct_3,plain,
    ( r2_hidden(c1_8_1__funct_3,k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3))
   => k1_funct_1(c3_8__funct_3,c1_8_1__funct_3) = k1_funct_1(c4_8__funct_3,c1_8_1__funct_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c1_8_1__funct_3,dt_c2_8__funct_3,e2_8__funct_3]),discharge_asm(discharge,[e1_8_1__funct_3])],[e1_8_1__funct_3,i2_8_1__funct_3]),
    [interesting(0.65),file(funct_3,i1_8_1__funct_3),[file(funct_3,i1_8_1__funct_3)]]).

fof(i1_8_1_tmp__funct_3,plain,
    ( r2_hidden(c1_8_1__funct_3,k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3))
   => k1_funct_1(c3_8__funct_3,c1_8_1__funct_3) = k1_funct_1(c4_8__funct_3,c1_8_1__funct_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c2_8__funct_3,e2_8__funct_3]),discharge_asm(discharge,[dt_c1_8_1__funct_3])],[dt_c1_8_1__funct_3,i1_8_1__funct_3]),
    [interesting(0.8),e3_8__funct_3]).

fof(e3_8__funct_3,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3))
     => k1_funct_1(c3_8__funct_3,A) = k1_funct_1(c4_8__funct_3,A) ) ),
    inference(let,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c2_8__funct_3,e2_8__funct_3])],[i1_8_1_tmp__funct_3,dh_c1_8_1__funct_3]),
    [interesting(0.8),file(funct_3,e3_8__funct_3),[file(funct_3,e3_8__funct_3)]]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.9),axiom,file(funct_1,t9_funct_1)]).

fof(e4_8__funct_3,plain,(
    c3_8__funct_3 = c4_8__funct_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c2_8__funct_3,e2_8__funct_3,e1_8__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_zfmisc_1,dt_c1_8__funct_3,dt_c2_8__funct_3,dt_c3_8__funct_3,dt_c4_8__funct_3,rc1_funct_1,t1_subset,t7_boole,e3_8__funct_3,e1_8__funct_3,t9_funct_1]),
    [interesting(0.8),file(funct_3,e4_8__funct_3),[file(funct_3,e4_8__funct_3)]]).

fof(i5_8__funct_3,theorem,(
    $true ),
    introduced(tautology,[file(funct_3,i5_8__funct_3)]),
    [interesting(0.8),trivial,file(funct_3,i5_8__funct_3)]).

fof(i4_8__funct_3,plain,(
    c3_8__funct_3 = c4_8__funct_3 ),
    inference(conclusion,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c2_8__funct_3,e2_8__funct_3,e1_8__funct_3])],[e4_8__funct_3,i5_8__funct_3]),
    [interesting(0.8),file(funct_3,i4_8__funct_3),[file(funct_3,i4_8__funct_3)]]).

fof(i3_8__funct_3,plain,
    ( ( k1_relat_1(c3_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
      & k1_relat_1(c4_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
      & ! [A,B] : 
          ( ( r2_hidden(A,c1_8__funct_3)
            & r2_hidden(B,c2_8__funct_3) )
         => k1_funct_1(c3_8__funct_3,k4_tarski(A,B)) = k1_funct_1(c4_8__funct_3,k4_tarski(A,B)) ) )
   => c3_8__funct_3 = c4_8__funct_3 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_8__funct_3,dt_c4_8__funct_3,dt_c1_8__funct_3,dt_c2_8__funct_3]),discharge_asm(discharge,[e1_8__funct_3,e2_8__funct_3])],[e1_8__funct_3,e2_8__funct_3,i4_8__funct_3]),
    [interesting(0.8),file(funct_3,i3_8__funct_3),[file(funct_3,i3_8__funct_3)]]).

fof(i3_8_tmp__funct_3,plain,
    ( ( v1_relat_1(c3_8__funct_3)
      & v1_funct_1(c3_8__funct_3)
      & v1_relat_1(c4_8__funct_3)
      & v1_funct_1(c4_8__funct_3) )
   => ( ( k1_relat_1(c3_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
        & k1_relat_1(c4_8__funct_3) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
        & ! [A,B] : 
            ( ( r2_hidden(A,c1_8__funct_3)
              & r2_hidden(B,c2_8__funct_3) )
           => k1_funct_1(c3_8__funct_3,k4_tarski(A,B)) = k1_funct_1(c4_8__funct_3,k4_tarski(A,B)) ) )
     => c3_8__funct_3 = c4_8__funct_3 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__funct_3,dt_c2_8__funct_3]),discharge_asm(discharge,[dt_c3_8__funct_3,dt_c4_8__funct_3])],[dt_c3_8__funct_3,dt_c4_8__funct_3,i3_8__funct_3]),
    [interesting(0.8),i2_8__funct_3]).

fof(i2_8__funct_3,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
              & k1_relat_1(B) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
              & ! [C,D] : 
                  ( ( r2_hidden(C,c1_8__funct_3)
                    & r2_hidden(D,c2_8__funct_3) )
                 => k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(C,D)) ) )
           => A = B ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__funct_3,dt_c2_8__funct_3])],[i3_8_tmp__funct_3,dh_c3_8__funct_3,dh_c4_8__funct_3]),
    [interesting(0.8),file(funct_3,i2_8__funct_3),[file(funct_3,i2_8__funct_3)]]).

fof(i2_8_tmp__funct_3,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
              & k1_relat_1(B) = k2_zfmisc_1(c1_8__funct_3,c2_8__funct_3)
              & ! [C,D] : 
                  ( ( r2_hidden(C,c1_8__funct_3)
                    & r2_hidden(D,c2_8__funct_3) )
                 => k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(C,D)) ) )
           => A = B ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__funct_3]),discharge_asm(discharge,[dt_c2_8__funct_3])],[dt_c2_8__funct_3,i2_8__funct_3]),
    [interesting(0.8),i1_8__funct_3]).

fof(i1_8__funct_3,plain,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( k1_relat_1(B) = k2_zfmisc_1(c1_8__funct_3,A)
              & k1_relat_1(C) = k2_zfmisc_1(c1_8__funct_3,A)
              & ! [D,E] : 
                  ( ( r2_hidden(D,c1_8__funct_3)
                    & r2_hidden(E,A) )
                 => k1_funct_1(B,k4_tarski(D,E)) = k1_funct_1(C,k4_tarski(D,E)) ) )
           => B = C ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__funct_3])],[i2_8_tmp__funct_3,dh_c2_8__funct_3]),
    [interesting(0.8),file(funct_3,i1_8__funct_3),[file(funct_3,i1_8__funct_3)]]).

fof(i1_8_tmp__funct_3,plain,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( k1_relat_1(B) = k2_zfmisc_1(c1_8__funct_3,A)
              & k1_relat_1(C) = k2_zfmisc_1(c1_8__funct_3,A)
              & ! [D,E] : 
                  ( ( r2_hidden(D,c1_8__funct_3)
                    & r2_hidden(E,A) )
                 => k1_funct_1(B,k4_tarski(D,E)) = k1_funct_1(C,k4_tarski(D,E)) ) )
           => B = C ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__funct_3])],[dt_c1_8__funct_3,i1_8__funct_3]),
    [interesting(1),t6_funct_3]).

fof(t6_funct_3,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( k1_relat_1(C) = k2_zfmisc_1(A,B)
              & k1_relat_1(D) = k2_zfmisc_1(A,B)
              & ! [E,F] : 
                  ( ( r2_hidden(E,A)
                    & r2_hidden(F,B) )
                 => k1_funct_1(C,k4_tarski(E,F)) = k1_funct_1(D,k4_tarski(E,F)) ) )
           => C = D ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__funct_3,dh_c1_8__funct_3]),
    [interesting(1),file(funct_3,t6_funct_3),[file(funct_3,t6_funct_3)]]).