% Mizar ND problem: t59_funct_6,funct_6,1341,71 
fof(dh_c1_65__funct_6,definition,
    ( ( ( v1_relat_1(c1_65__funct_6)
        & v1_funct_1(c1_65__funct_6) )
     => ( ~ r2_hidden(k1_xboole_0,k2_relat_1(c1_65__funct_6))
       => ( v2_funct_1(k7_funct_6(c1_65__funct_6))
        <=> ! [A] : 
              ( ( v1_relat_1(A)
                & v1_funct_1(A) )
             => ( r2_hidden(A,k2_relat_1(c1_65__funct_6))
               => v2_funct_1(A) ) ) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ( ~ r2_hidden(k1_xboole_0,k2_relat_1(B))
         => ( v2_funct_1(k7_funct_6(B))
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( r2_hidden(C,k2_relat_1(B))
                 => v2_funct_1(C) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_65__funct_6),file(funct_6,c1_65__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_65__funct_6)]).

fof(e1_65__funct_6,assumption,(
    ~ r2_hidden(k1_xboole_0,k2_relat_1(c1_65__funct_6)) ),
    introduced(assumption,[file(funct_6,e1_65__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,e1_65__funct_6)]).

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_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k7_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_funct_6(A))
        & v1_funct_1(k7_funct_6(A)) ) ) ),
    file(funct_6,k7_funct_6),
    [interesting(0.9),axiom,file(funct_6,k7_funct_6)]).

fof(dt_c1_65__funct_6,assumption,
    ( v1_relat_1(c1_65__funct_6)
    & v1_funct_1(c1_65__funct_6) ),
    introduced(assumption,[file(funct_6,c1_65__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_65__funct_6)]).

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(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(e1_65_2__funct_6,assumption,(
    ! [A,B] : 
      ( ( r2_hidden(A,k1_relat_1(k7_funct_6(c1_65__funct_6)))
        & r2_hidden(B,k1_relat_1(k7_funct_6(c1_65__funct_6)))
        & k1_funct_1(k7_funct_6(c1_65__funct_6),A) = k1_funct_1(k7_funct_6(c1_65__funct_6),B) )
     => A = B ) ),
    introduced(assumption,[file(funct_6,e1_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_65_2__funct_6)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.9),axiom,file(funct_1,d8_funct_1)]).

fof(dh_c1_65_2__funct_6,definition,
    ( ( ( v1_relat_1(c1_65_2__funct_6)
        & v1_funct_1(c1_65_2__funct_6) )
     => ( r2_hidden(c1_65_2__funct_6,k2_relat_1(c1_65__funct_6))
       => v2_funct_1(c1_65_2__funct_6) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(A,k2_relat_1(c1_65__funct_6))
         => v2_funct_1(A) ) ) ),
    introduced(definition,[new_symbol(c1_65_2__funct_6),file(funct_6,c1_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_65_2__funct_6)]).

fof(e2_65_2__funct_6,assumption,(
    r2_hidden(c1_65_2__funct_6,k2_relat_1(c1_65__funct_6)) ),
    introduced(assumption,[file(funct_6,e2_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e2_65_2__funct_6)]).

fof(dt_c1_65_2__funct_6,assumption,
    ( v1_relat_1(c1_65_2__funct_6)
    & v1_funct_1(c1_65_2__funct_6) ),
    introduced(assumption,[file(funct_6,c1_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_65_2__funct_6)]).

fof(dt_c3_65_2__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c3_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c3_65_2__funct_6)]).

fof(dh_c3_65_2__funct_6,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c3_65_2__funct_6,k1_relat_1(c1_65_2__funct_6))
          & r2_hidden(A,k1_relat_1(c1_65_2__funct_6))
          & k1_funct_1(c1_65_2__funct_6,c3_65_2__funct_6) = k1_funct_1(c1_65_2__funct_6,A)
          & c3_65_2__funct_6 != A )
   => ! [B,C] : 
        ~ ( r2_hidden(B,k1_relat_1(c1_65_2__funct_6))
          & r2_hidden(C,k1_relat_1(c1_65_2__funct_6))
          & k1_funct_1(c1_65_2__funct_6,B) = k1_funct_1(c1_65_2__funct_6,C)
          & B != C ) ),
    introduced(definition,[new_symbol(c3_65_2__funct_6),file(funct_6,c3_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c3_65_2__funct_6)]).

fof(dh_c4_65_2__funct_6,definition,
    ( ~ ( r2_hidden(c3_65_2__funct_6,k1_relat_1(c1_65_2__funct_6))
        & r2_hidden(c4_65_2__funct_6,k1_relat_1(c1_65_2__funct_6))
        & k1_funct_1(c1_65_2__funct_6,c3_65_2__funct_6) = k1_funct_1(c1_65_2__funct_6,c4_65_2__funct_6)
        & c3_65_2__funct_6 != c4_65_2__funct_6 )
   => ! [A] : 
        ~ ( r2_hidden(c3_65_2__funct_6,k1_relat_1(c1_65_2__funct_6))
          & r2_hidden(A,k1_relat_1(c1_65_2__funct_6))
          & k1_funct_1(c1_65_2__funct_6,c3_65_2__funct_6) = k1_funct_1(c1_65_2__funct_6,A)
          & c3_65_2__funct_6 != A ) ),
    introduced(definition,[new_symbol(c4_65_2__funct_6),file(funct_6,c4_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c4_65_2__funct_6)]).

fof(e12_65_2__funct_6,assumption,
    ( r2_hidden(c3_65_2__funct_6,k1_relat_1(c1_65_2__funct_6))
    & r2_hidden(c4_65_2__funct_6,k1_relat_1(c1_65_2__funct_6))
    & k1_funct_1(c1_65_2__funct_6,c3_65_2__funct_6) = k1_funct_1(c1_65_2__funct_6,c4_65_2__funct_6) ),
    introduced(assumption,[file(funct_6,e12_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e12_65_2__funct_6)]).

fof(dh_c2_65_2__funct_6,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_65__funct_6))
        & c1_65_2__funct_6 = k1_funct_1(c1_65__funct_6,A) )
   => ( r2_hidden(c2_65_2__funct_6,k1_relat_1(c1_65__funct_6))
      & c1_65_2__funct_6 = k1_funct_1(c1_65__funct_6,c2_65_2__funct_6) ) ),
    introduced(definition,[new_symbol(c2_65_2__funct_6),file(funct_6,c2_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c2_65_2__funct_6)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

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(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_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(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

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(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(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(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_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(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_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(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(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(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(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e3_65_2__funct_6,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_65__funct_6))
      & c1_65_2__funct_6 = k1_funct_1(c1_65__funct_6,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_65__funct_6,dt_c1_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,e2_65_2__funct_6,d5_funct_1]),
    [interesting(0.65),file(funct_6,e3_65_2__funct_6),[file(funct_6,e3_65_2__funct_6)]]).

fof(dt_c2_65_2__funct_6,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6])],[dh_c2_65_2__funct_6,e3_65_2__funct_6]),
    [interesting(0.65),file(funct_6,c2_65_2__funct_6),[file(funct_6,c2_65_2__funct_6)]]).

fof(dt_c4_65_2__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c4_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c4_65_2__funct_6)]).

fof(dh_c5_65_2__funct_6,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
        & ! [B] : 
            ( r2_hidden(B,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
           => ( ( B = c2_65_2__funct_6
               => k1_funct_1(A,B) = c3_65_2__funct_6 )
              & ( B != c2_65_2__funct_6
               => k1_funct_1(A,B) = k1_funct_1(c3_65__funct_6,B) ) ) ) )
   => ( v1_relat_1(c5_65_2__funct_6)
      & v1_funct_1(c5_65_2__funct_6)
      & k1_relat_1(c5_65_2__funct_6) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [C] : 
          ( r2_hidden(C,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
         => ( ( C = c2_65_2__funct_6
             => k1_funct_1(c5_65_2__funct_6,C) = c3_65_2__funct_6 )
            & ( C != c2_65_2__funct_6
             => k1_funct_1(c5_65_2__funct_6,C) = k1_funct_1(c3_65__funct_6,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c5_65_2__funct_6),file(funct_6,c5_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c5_65_2__funct_6)]).

fof(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_1)]).

fof(dt_k1_funct_6,axiom,(
    $true ),
    file(funct_6,k1_funct_6),
    [interesting(0.9),axiom,file(funct_6,k1_funct_6)]).

fof(dh_c3_65__funct_6,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & c2_65__funct_6 = A
        & k1_relat_1(A) = k1_relat_1(k2_funct_6(c1_65__funct_6))
        & ! [B] : 
            ( r2_hidden(B,k1_relat_1(k2_funct_6(c1_65__funct_6)))
           => r2_hidden(k1_funct_1(A,B),k1_funct_1(k2_funct_6(c1_65__funct_6),B)) ) )
   => ( v1_relat_1(c3_65__funct_6)
      & v1_funct_1(c3_65__funct_6)
      & c2_65__funct_6 = c3_65__funct_6
      & k1_relat_1(c3_65__funct_6) = k1_relat_1(k2_funct_6(c1_65__funct_6))
      & ! [C] : 
          ( r2_hidden(C,k1_relat_1(k2_funct_6(c1_65__funct_6)))
         => r2_hidden(k1_funct_1(c3_65__funct_6,C),k1_funct_1(k2_funct_6(c1_65__funct_6),C)) ) ) ),
    introduced(definition,[new_symbol(c3_65__funct_6),file(funct_6,c3_65__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_65__funct_6)]).

fof(dt_k2_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A)) ) ) ),
    file(funct_6,k2_funct_6),
    [interesting(0.9),axiom,file(funct_6,k2_funct_6)]).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    [interesting(0.9),axiom,file(card_3,k4_card_3)]).

fof(dh_c2_65__funct_6,definition,
    ( ? [A] : m1_subset_1(A,k4_card_3(k2_funct_6(c1_65__funct_6)))
   => m1_subset_1(c2_65__funct_6,k4_card_3(k2_funct_6(c1_65__funct_6))) ),
    introduced(definition,[new_symbol(c2_65__funct_6),file(funct_6,c2_65__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_65__funct_6)]).

fof(e4_65__funct_6,plain,(
    ? [A] : m1_subset_1(A,k4_card_3(k2_funct_6(c1_65__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6])],[rc1_funct_1,existence_m1_subset_1,dt_k2_funct_6,dt_k4_card_3,dt_m1_subset_1,dt_c1_65__funct_6]),
    [interesting(0.8),file(funct_6,e4_65__funct_6),[file(funct_6,e4_65__funct_6)]]).

fof(dt_c2_65__funct_6,plain,(
    m1_subset_1(c2_65__funct_6,k4_card_3(k2_funct_6(c1_65__funct_6))) ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6])],[dh_c2_65__funct_6,e4_65__funct_6]),
    [interesting(0.8),file(funct_6,c2_65__funct_6),[file(funct_6,c2_65__funct_6)]]).

fof(e1_65_1__funct_6,assumption,(
    r2_hidden(k1_xboole_0,k2_relat_1(k2_funct_6(c1_65__funct_6))) ),
    introduced(assumption,[file(funct_6,e1_65_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,e1_65_1__funct_6)]).

fof(dh_c1_65_1__funct_6,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
        & k1_xboole_0 = k1_funct_1(k2_funct_6(c1_65__funct_6),A) )
   => ( r2_hidden(c1_65_1__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
      & k1_xboole_0 = k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_1__funct_6) ) ),
    introduced(definition,[new_symbol(c1_65_1__funct_6),file(funct_6,c1_65_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c1_65_1__funct_6)]).

fof(e2_65_1__funct_6,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
      & k1_xboole_0 = k1_funct_1(k2_funct_6(c1_65__funct_6),A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funct_6,dt_k2_relat_1,dt_c1_65__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,e1_65_1__funct_6,d5_funct_1]),
    [interesting(0.65),file(funct_6,e2_65_1__funct_6),[file(funct_6,e2_65_1__funct_6)]]).

fof(dt_c1_65_1__funct_6,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[dh_c1_65_1__funct_6,e2_65_1__funct_6]),
    [interesting(0.65),file(funct_6,c1_65_1__funct_6),[file(funct_6,c1_65_1__funct_6)]]).

fof(de_c2_65_1__funct_6,definition,(
    c2_65_1__funct_6 = k1_funct_1(c1_65__funct_6,c1_65_1__funct_6) ),
    introduced(definition,[new_symbol(c2_65_1__funct_6),file(funct_6,c2_65_1__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c2_65_1__funct_6)]).

fof(fc18_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k10_relat_1(A,B)) ) ),
    file(finseq_1,fc18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc18_finseq_1)]).

fof(dt_k1_funct_5,axiom,(
    $true ),
    file(funct_5,k1_funct_5),
    [interesting(0.9),axiom,file(funct_5,k1_funct_5)]).

fof(e3_65_1__funct_6,plain,
    ( r2_hidden(c1_65_1__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
    & k1_xboole_0 = k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_1__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[dh_c1_65_1__funct_6,e2_65_1__funct_6]),
    [interesting(0.65),file(funct_6,e3_65_1__funct_6),[file(funct_6,e3_65_1__funct_6)]]).

fof(d2_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_funct_6(A)
          <=> ( k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
              & ! [C] : 
                  ( r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
                 => k1_funct_1(B,C) = k1_funct_5(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(funct_6,d2_funct_6),
    [interesting(0.9),axiom,file(funct_6,d2_funct_6)]).

fof(e4_65_1__funct_6,plain,(
    r2_hidden(c1_65_1__funct_6,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_5,dt_k1_funct_6,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funct_6,dt_k2_relat_1,dt_c1_65__funct_6,dt_c1_65_1__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,e3_65_1__funct_6,d2_funct_6]),
    [interesting(0.65),file(funct_6,e4_65_1__funct_6),[file(funct_6,e4_65_1__funct_6)]]).

fof(d13_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    [interesting(0.9),axiom,file(funct_1,d13_funct_1)]).

fof(e5_65_1__funct_6,plain,
    ( r2_hidden(c1_65_1__funct_6,k1_relat_1(c1_65__funct_6))
    & r2_hidden(k1_funct_1(c1_65__funct_6,c1_65_1__funct_6),k1_funct_6(k2_relat_1(c1_65__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_c1_65__funct_6,dt_c1_65_1__funct_6,rc1_funct_1,t1_subset,t7_boole,e4_65_1__funct_6,d13_funct_1]),
    [interesting(0.65),file(funct_6,e5_65_1__funct_6),[file(funct_6,e5_65_1__funct_6)]]).

fof(d1_funct_6,definition,(
    ! [A,B] : 
      ( B = k1_funct_6(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ( r2_hidden(C,A)
            & v1_relat_1(C)
            & v1_funct_1(C) ) ) ) ),
    file(funct_6,d1_funct_6),
    [interesting(0.9),axiom,file(funct_6,d1_funct_6)]).

fof(e6_65_1__funct_6,plain,
    ( v1_relat_1(k1_funct_1(c1_65__funct_6,c1_65_1__funct_6))
    & v1_funct_1(k1_funct_1(c1_65__funct_6,c1_65_1__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_c1_65__funct_6,dt_c1_65_1__funct_6,rc1_funct_1,t1_subset,t7_boole,e5_65_1__funct_6,d1_funct_6]),
    [interesting(0.65),file(funct_6,e6_65_1__funct_6),[file(funct_6,e6_65_1__funct_6)]]).

fof(dt_c2_65_1__funct_6,plain,
    ( v1_relat_1(c2_65_1__funct_6)
    & v1_funct_1(c2_65_1__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[dt_k1_funct_1,dt_c1_65__funct_6,dt_c1_65_1__funct_6,rc1_funct_1,de_c2_65_1__funct_6,e6_65_1__funct_6]),
    [interesting(0.65),file(funct_6,c2_65_1__funct_6),[file(funct_6,c2_65_1__funct_6)]]).

fof(dt_k3_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_6(A))
        & v1_funct_1(k3_funct_6(A)) ) ) ),
    file(funct_6,k3_funct_6),
    [interesting(0.9),axiom,file(funct_6,k3_funct_6)]).

fof(t31_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(B))
              & C = k1_funct_1(B,A) )
           => ( r2_hidden(A,k1_relat_1(k2_funct_6(B)))
              & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C)
              & r2_hidden(A,k1_relat_1(k3_funct_6(B)))
              & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ),
    file(funct_6,t31_funct_6),
    [interesting(0.9),axiom,file(funct_6,t31_funct_6)]).

fof(e7_65_1__funct_6,plain,
    ( k1_xboole_0 = k1_relat_1(c2_65_1__funct_6)
    & r2_hidden(c2_65_1__funct_6,k2_relat_1(c1_65__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_c1_65__funct_6,dt_c1_65_1__funct_6,dt_c2_65_1__funct_6,de_c2_65_1__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,e3_65_1__funct_6,e5_65_1__funct_6,t31_funct_6,d5_funct_1]),
    [interesting(0.65),file(funct_6,e7_65_1__funct_6),[file(funct_6,e7_65_1__funct_6)]]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.9),axiom,file(relat_1,t64_relat_1)]).

fof(e8_65_1__funct_6,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6,e1_65__funct_6])],[existence_m1_subset_1,dt_k1_funct_1,dt_m1_subset_1,dt_c1_65_1__funct_6,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc17_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_65__funct_6,dt_c2_65_1__funct_6,de_c2_65_1__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,t1_subset,t6_boole,t7_boole,e7_65_1__funct_6,e1_65__funct_6,t64_relat_1]),
    [interesting(0.65),file(funct_6,e8_65_1__funct_6),[file(funct_6,e8_65_1__funct_6)]]).

fof(i2_65_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i2_65_1__funct_6)]),
    [interesting(0.65),trivial,file(funct_6,i2_65_1__funct_6)]).

fof(i1_65_1__funct_6,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c1_65__funct_6,e1_65_1__funct_6,e1_65__funct_6])],[e8_65_1__funct_6,i2_65_1__funct_6]),
    [interesting(0.65),file(funct_6,i1_65_1__funct_6),[file(funct_6,i1_65_1__funct_6)]]).

fof(e2_65__funct_6,plain,(
    ~ r2_hidden(k1_xboole_0,k2_relat_1(k2_funct_6(c1_65__funct_6))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_65__funct_6,e1_65__funct_6]),discharge_asm(discharge,[e1_65_1__funct_6])],[e1_65_1__funct_6,i1_65_1__funct_6]),
    [interesting(0.8),file(funct_6,e2_65__funct_6),[file(funct_6,e2_65__funct_6)]]).

fof(t37_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    file(card_3,t37_card_3),
    [interesting(0.9),axiom,file(card_3,t37_card_3)]).

fof(e3_65__funct_6,plain,(
    k4_card_3(k2_funct_6(c1_65__funct_6)) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_c1_65__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,e2_65__funct_6,t37_card_3]),
    [interesting(0.8),file(funct_6,e3_65__funct_6),[file(funct_6,e3_65__funct_6)]]).

fof(d5_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    [interesting(0.9),axiom,file(card_3,d5_card_3)]).

fof(e5_65__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & c2_65__funct_6 = A
      & k1_relat_1(A) = k1_relat_1(k2_funct_6(c1_65__funct_6))
      & ! [B] : 
          ( r2_hidden(B,k1_relat_1(k2_funct_6(c1_65__funct_6)))
         => r2_hidden(k1_funct_1(A,B),k1_funct_1(k2_funct_6(c1_65__funct_6),B)) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6,e1_65__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc17_finseq_1,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funct_6,dt_k4_card_3,dt_c1_65__funct_6,dt_c2_65__funct_6,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,t1_subset,t6_boole,t7_boole,e3_65__funct_6,d5_card_3]),
    [interesting(0.8),file(funct_6,e5_65__funct_6),[file(funct_6,e5_65__funct_6)]]).

fof(dt_c3_65__funct_6,plain,
    ( v1_relat_1(c3_65__funct_6)
    & v1_funct_1(c3_65__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6,e1_65__funct_6])],[dh_c3_65__funct_6,e5_65__funct_6]),
    [interesting(0.8),file(funct_6,c3_65__funct_6),[file(funct_6,c3_65__funct_6)]]).

fof(s1_partfun1__e8_65_2__funct_6,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ? [E] : 
          ( v1_relat_1(E)
          & v1_funct_1(E)
          & k1_relat_1(E) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
          & ! [F] : 
              ( r2_hidden(F,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
             => ( ( F = C
                 => k1_funct_1(E,F) = D )
                & ( F != C
                 => k1_funct_1(E,F) = k1_funct_1(B,F) ) ) ) ) ) ),
    file(funct_6,s1_partfun1__e8_65_2__funct_6),
    [interesting(0.9),axiom,file(funct_6,s1_partfun1__e8_65_2__funct_6)]).

fof(e8_65_2__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [B] : 
          ( r2_hidden(B,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
         => ( ( B = c2_65_2__funct_6
             => k1_funct_1(A,B) = c3_65_2__funct_6 )
            & ( B != c2_65_2__funct_6
             => k1_funct_1(A,B) = k1_funct_1(c3_65__funct_6,B) ) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_c1_65__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c3_65_2__funct_6,rc1_funct_1,s1_partfun1__e8_65_2__funct_6]),
    [interesting(0.65),file(funct_6,e8_65_2__funct_6),[file(funct_6,e8_65_2__funct_6)]]).

fof(dt_c5_65_2__funct_6,plain,
    ( v1_relat_1(c5_65_2__funct_6)
    & v1_funct_1(c5_65_2__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[dh_c5_65_2__funct_6,e8_65_2__funct_6]),
    [interesting(0.65),file(funct_6,c5_65_2__funct_6),[file(funct_6,c5_65_2__funct_6)]]).

fof(dh_c6_65_2__funct_6,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
        & ! [B] : 
            ( r2_hidden(B,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
           => ( ( B = c2_65_2__funct_6
               => k1_funct_1(A,B) = c4_65_2__funct_6 )
              & ( B != c2_65_2__funct_6
               => k1_funct_1(A,B) = k1_funct_1(c3_65__funct_6,B) ) ) ) )
   => ( v1_relat_1(c6_65_2__funct_6)
      & v1_funct_1(c6_65_2__funct_6)
      & k1_relat_1(c6_65_2__funct_6) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [C] : 
          ( r2_hidden(C,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
         => ( ( C = c2_65_2__funct_6
             => k1_funct_1(c6_65_2__funct_6,C) = c4_65_2__funct_6 )
            & ( C != c2_65_2__funct_6
             => k1_funct_1(c6_65_2__funct_6,C) = k1_funct_1(c3_65__funct_6,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c6_65_2__funct_6),file(funct_6,c6_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c6_65_2__funct_6)]).

fof(s1_partfun1__e10_65_2__funct_6,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ? [E] : 
          ( v1_relat_1(E)
          & v1_funct_1(E)
          & k1_relat_1(E) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
          & ! [F] : 
              ( r2_hidden(F,k10_relat_1(A,k1_funct_6(k2_relat_1(A))))
             => ( ( F = C
                 => k1_funct_1(E,F) = D )
                & ( F != C
                 => k1_funct_1(E,F) = k1_funct_1(B,F) ) ) ) ) ) ),
    file(funct_6,s1_partfun1__e10_65_2__funct_6),
    [interesting(0.9),axiom,file(funct_6,s1_partfun1__e10_65_2__funct_6)]).

fof(e10_65_2__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [B] : 
          ( r2_hidden(B,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
         => ( ( B = c2_65_2__funct_6
             => k1_funct_1(A,B) = c4_65_2__funct_6 )
            & ( B != c2_65_2__funct_6
             => k1_funct_1(A,B) = k1_funct_1(c3_65__funct_6,B) ) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_relat_1,dt_c1_65__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c4_65_2__funct_6,rc1_funct_1,s1_partfun1__e10_65_2__funct_6]),
    [interesting(0.65),file(funct_6,e10_65_2__funct_6),[file(funct_6,e10_65_2__funct_6)]]).

fof(dt_c6_65_2__funct_6,plain,
    ( v1_relat_1(c6_65_2__funct_6)
    & v1_funct_1(c6_65_2__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[dh_c6_65_2__funct_6,e10_65_2__funct_6]),
    [interesting(0.65),file(funct_6,c6_65_2__funct_6),[file(funct_6,c6_65_2__funct_6)]]).

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_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_funct_5(A))
        & v1_funct_1(k4_funct_5(A)) ) ) ),
    file(funct_5,k4_funct_5),
    [interesting(0.9),axiom,file(funct_5,k4_funct_5)]).

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

fof(dh_c7_65_2__funct_6,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_funct_1(k7_funct_6(c1_65__funct_6),c5_65_2__funct_6) = A
        & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
        & ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => k1_funct_1(A,B) = k1_funct_1(k4_funct_5(c1_65__funct_6),k4_tarski(B,k1_funct_1(c5_65_2__funct_6,B))) ) )
   => ( v1_relat_1(c7_65_2__funct_6)
      & v1_funct_1(c7_65_2__funct_6)
      & k1_funct_1(k7_funct_6(c1_65__funct_6),c5_65_2__funct_6) = c7_65_2__funct_6
      & k1_relat_1(c7_65_2__funct_6) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [C] : 
          ( r2_hidden(C,k1_relat_1(c7_65_2__funct_6))
         => k1_funct_1(c7_65_2__funct_6,C) = k1_funct_1(k4_funct_5(c1_65__funct_6),k4_tarski(C,k1_funct_1(c5_65_2__funct_6,C))) ) ) ),
    introduced(definition,[new_symbol(c7_65_2__funct_6),file(funct_6,c7_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c7_65_2__funct_6)]).

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(dh_c1_65_2_1__funct_6,definition,
    ( ( r2_hidden(c1_65_2_1__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
     => r2_hidden(k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_1__funct_6)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
       => r2_hidden(k1_funct_1(c5_65_2__funct_6,A),k1_funct_1(k2_funct_6(c1_65__funct_6),A)) ) ),
    introduced(definition,[new_symbol(c1_65_2_1__funct_6),file(funct_6,c1_65_2_1__funct_6)]),
    [interesting(0.5),axiom,file(funct_6,c1_65_2_1__funct_6)]).

fof(e1_65_2_1__funct_6,assumption,(
    r2_hidden(c1_65_2_1__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6))) ),
    introduced(assumption,[file(funct_6,e1_65_2_1__funct_6)]),
    [interesting(0.5),axiom,file(funct_6,e1_65_2_1__funct_6)]).

fof(dt_c1_65_2_1__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_65_2_1__funct_6)]),
    [interesting(0.5),axiom,file(funct_6,c1_65_2_1__funct_6)]).

fof(e6_65__funct_6,plain,
    ( c2_65__funct_6 = c3_65__funct_6
    & k1_relat_1(c3_65__funct_6) = k1_relat_1(k2_funct_6(c1_65__funct_6))
    & ! [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
       => r2_hidden(k1_funct_1(c3_65__funct_6,A),k1_funct_1(k2_funct_6(c1_65__funct_6),A)) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6,e1_65__funct_6])],[dh_c3_65__funct_6,e5_65__funct_6]),
    [interesting(0.8),file(funct_6,e6_65__funct_6),[file(funct_6,e6_65__funct_6)]]).

fof(d7_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k7_funct_6(A)
          <=> ( k1_relat_1(B) = k4_card_3(k2_funct_6(A))
              & ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C) )
                 => ~ ( r2_hidden(C,k4_card_3(k2_funct_6(A)))
                      & ! [D] : 
                          ( ( v1_relat_1(D)
                            & v1_funct_1(D) )
                         => ~ ( k1_funct_1(B,C) = D
                              & k1_relat_1(D) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))
                              & ! [E] : 
                                  ( r2_hidden(E,k1_relat_1(D))
                                 => k1_funct_1(D,E) = k1_funct_1(k4_funct_5(A),k4_tarski(E,k1_funct_1(C,E))) ) ) ) ) ) ) ) ) ) ),
    file(funct_6,d7_funct_6),
    [interesting(0.9),axiom,file(funct_6,d7_funct_6)]).

fof(e7_65__funct_6,plain,
    ( k1_relat_1(k2_funct_6(c1_65__funct_6)) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
    & k1_relat_1(k7_funct_6(c1_65__funct_6)) = k4_card_3(k2_funct_6(c1_65__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,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,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_5,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k4_funct_5,dt_k4_tarski,dt_k7_funct_6,dt_c1_65__funct_6,rc1_funct_1,t1_subset,t7_boole,d5_tarski,d2_funct_6,d7_funct_6]),
    [interesting(0.8),file(funct_6,e7_65__funct_6),[file(funct_6,e7_65__funct_6)]]).

fof(e9_65_2__funct_6,plain,
    ( k1_relat_1(c5_65_2__funct_6) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
    & ! [A] : 
        ( r2_hidden(A,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
       => ( ( A = c2_65_2__funct_6
           => k1_funct_1(c5_65_2__funct_6,A) = c3_65_2__funct_6 )
          & ( A != c2_65_2__funct_6
           => k1_funct_1(c5_65_2__funct_6,A) = k1_funct_1(c3_65__funct_6,A) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[dh_c5_65_2__funct_6,e8_65_2__funct_6]),
    [interesting(0.65),file(funct_6,e9_65_2__funct_6),[file(funct_6,e9_65_2__funct_6)]]).

fof(e2_65_2_1__funct_6,plain,
    ( ( c1_65_2_1__funct_6 = c2_65_2__funct_6
     => k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6) = c3_65_2__funct_6 )
    & ( c1_65_2_1__funct_6 != c2_65_2__funct_6
     => k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6) = k1_funct_1(c3_65__funct_6,c1_65_2_1__funct_6) )
    & r2_hidden(k1_funct_1(c3_65__funct_6,c1_65_2_1__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_1__funct_6))
    & ~ ( c1_65_2_1__funct_6 != c2_65_2__funct_6
        & c1_65_2_1__funct_6 = c2_65_2__funct_6 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65_2_1__funct_6,e1_65_2_1__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k7_funct_6,dt_c1_65__funct_6,dt_c1_65_2_1__funct_6,dt_c2_65__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c3_65_2__funct_6,dt_c5_65_2__funct_6,t1_subset,t7_boole,e1_65_2_1__funct_6,e6_65__funct_6,e7_65__funct_6,e9_65_2__funct_6]),
    [interesting(0.5),file(funct_6,e2_65_2_1__funct_6),[file(funct_6,e2_65_2_1__funct_6)]]).

fof(e4_65_2__funct_6,plain,
    ( r2_hidden(c2_65_2__funct_6,k1_relat_1(c1_65__funct_6))
    & c1_65_2__funct_6 = k1_funct_1(c1_65__funct_6,c2_65_2__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6])],[dh_c2_65_2__funct_6,e3_65_2__funct_6]),
    [interesting(0.65),file(funct_6,e4_65_2__funct_6),[file(funct_6,e4_65_2__funct_6)]]).

fof(e3_65_2_1__funct_6,plain,(
    r2_hidden(k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_1__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_65_2__funct_6,dt_c1_65_2_1__funct_6,e1_65_2_1__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,dt_c1_65_2_1__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c3_65_2__funct_6,dt_c4_65_2__funct_6,dt_c5_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,e2_65_2_1__funct_6,e4_65_2__funct_6,e12_65_2__funct_6,t31_funct_6]),
    [interesting(0.5),file(funct_6,e3_65_2_1__funct_6),[file(funct_6,e3_65_2_1__funct_6)]]).

fof(i3_65_2_1__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_65_2_1__funct_6)]),
    [interesting(0.5),trivial,file(funct_6,i3_65_2_1__funct_6)]).

fof(i2_65_2_1__funct_6,plain,(
    r2_hidden(k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_1__funct_6)) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_65_2__funct_6,dt_c1_65_2_1__funct_6,e1_65_2_1__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6])],[e3_65_2_1__funct_6,i3_65_2_1__funct_6]),
    [interesting(0.5),file(funct_6,i2_65_2_1__funct_6),[file(funct_6,i2_65_2_1__funct_6)]]).

fof(i1_65_2_1__funct_6,plain,
    ( r2_hidden(c1_65_2_1__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
   => r2_hidden(k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_1__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_65_2__funct_6,dt_c1_65_2_1__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6]),discharge_asm(discharge,[e1_65_2_1__funct_6])],[e1_65_2_1__funct_6,i2_65_2_1__funct_6]),
    [interesting(0.5),file(funct_6,i1_65_2_1__funct_6),[file(funct_6,i1_65_2_1__funct_6)]]).

fof(i1_65_2_1_tmp__funct_6,plain,
    ( r2_hidden(c1_65_2_1__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
   => r2_hidden(k1_funct_1(c5_65_2__funct_6,c1_65_2_1__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_1__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_65_2__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6]),discharge_asm(discharge,[dt_c1_65_2_1__funct_6])],[dt_c1_65_2_1__funct_6,i1_65_2_1__funct_6]),
    [interesting(0.65),e13_65_2__funct_6]).

fof(e13_65_2__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
     => r2_hidden(k1_funct_1(c5_65_2__funct_6,A),k1_funct_1(k2_funct_6(c1_65__funct_6),A)) ) ),
    inference(let,[status(thm),assumptions([dt_c4_65_2__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6])],[i1_65_2_1_tmp__funct_6,dh_c1_65_2_1__funct_6]),
    [interesting(0.65),file(funct_6,e13_65_2__funct_6),[file(funct_6,e13_65_2__funct_6)]]).

fof(e14_65_2__funct_6,plain,
    ( r2_hidden(c5_65_2__funct_6,k4_card_3(k2_funct_6(c1_65__funct_6)))
    & k1_relat_1(k7_funct_6(c1_65__funct_6)) = k4_card_3(k2_funct_6(c1_65__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_65_2__funct_6,e12_65_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k7_funct_6,dt_c1_65__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c3_65_2__funct_6,dt_c5_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,e13_65_2__funct_6,e7_65__funct_6,e9_65_2__funct_6,d5_card_3]),
    [interesting(0.65),file(funct_6,e14_65_2__funct_6),[file(funct_6,e14_65_2__funct_6)]]).

fof(e15_65_2__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_funct_1(k7_funct_6(c1_65__funct_6),c5_65_2__funct_6) = A
      & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k1_funct_1(A,B) = k1_funct_1(k4_funct_5(c1_65__funct_6),k4_tarski(B,k1_funct_1(c5_65_2__funct_6,B))) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_65_2__funct_6,e12_65_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,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,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k4_funct_5,dt_k4_tarski,dt_k7_funct_6,dt_c1_65__funct_6,dt_c5_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,d5_tarski,e14_65_2__funct_6,d7_funct_6]),
    [interesting(0.65),file(funct_6,e15_65_2__funct_6),[file(funct_6,e15_65_2__funct_6)]]).

fof(dt_c7_65_2__funct_6,plain,
    ( v1_relat_1(c7_65_2__funct_6)
    & v1_funct_1(c7_65_2__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c4_65_2__funct_6,e12_65_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c3_65_2__funct_6])],[dh_c7_65_2__funct_6,e15_65_2__funct_6]),
    [interesting(0.65),file(funct_6,c7_65_2__funct_6),[file(funct_6,c7_65_2__funct_6)]]).

fof(dh_c8_65_2__funct_6,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_funct_1(k7_funct_6(c1_65__funct_6),c6_65_2__funct_6) = A
        & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
        & ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => k1_funct_1(A,B) = k1_funct_1(k4_funct_5(c1_65__funct_6),k4_tarski(B,k1_funct_1(c6_65_2__funct_6,B))) ) )
   => ( v1_relat_1(c8_65_2__funct_6)
      & v1_funct_1(c8_65_2__funct_6)
      & k1_funct_1(k7_funct_6(c1_65__funct_6),c6_65_2__funct_6) = c8_65_2__funct_6
      & k1_relat_1(c8_65_2__funct_6) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [C] : 
          ( r2_hidden(C,k1_relat_1(c8_65_2__funct_6))
         => k1_funct_1(c8_65_2__funct_6,C) = k1_funct_1(k4_funct_5(c1_65__funct_6),k4_tarski(C,k1_funct_1(c6_65_2__funct_6,C))) ) ) ),
    introduced(definition,[new_symbol(c8_65_2__funct_6),file(funct_6,c8_65_2__funct_6)]),
    [interesting(0.65),axiom,file(funct_6,c8_65_2__funct_6)]).

fof(dh_c1_65_2_2__funct_6,definition,
    ( ( r2_hidden(c1_65_2_2__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
     => r2_hidden(k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_2__funct_6)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
       => r2_hidden(k1_funct_1(c6_65_2__funct_6,A),k1_funct_1(k2_funct_6(c1_65__funct_6),A)) ) ),
    introduced(definition,[new_symbol(c1_65_2_2__funct_6),file(funct_6,c1_65_2_2__funct_6)]),
    [interesting(0.5),axiom,file(funct_6,c1_65_2_2__funct_6)]).

fof(e1_65_2_2__funct_6,assumption,(
    r2_hidden(c1_65_2_2__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6))) ),
    introduced(assumption,[file(funct_6,e1_65_2_2__funct_6)]),
    [interesting(0.5),axiom,file(funct_6,e1_65_2_2__funct_6)]).

fof(dt_c1_65_2_2__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_65_2_2__funct_6)]),
    [interesting(0.5),axiom,file(funct_6,c1_65_2_2__funct_6)]).

fof(e11_65_2__funct_6,plain,
    ( k1_relat_1(c6_65_2__funct_6) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
    & ! [A] : 
        ( r2_hidden(A,k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6))))
       => ( ( A = c2_65_2__funct_6
           => k1_funct_1(c6_65_2__funct_6,A) = c4_65_2__funct_6 )
          & ( A != c2_65_2__funct_6
           => k1_funct_1(c6_65_2__funct_6,A) = k1_funct_1(c3_65__funct_6,A) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[dh_c6_65_2__funct_6,e10_65_2__funct_6]),
    [interesting(0.65),file(funct_6,e11_65_2__funct_6),[file(funct_6,e11_65_2__funct_6)]]).

fof(e2_65_2_2__funct_6,plain,
    ( ( c1_65_2_2__funct_6 = c2_65_2__funct_6
     => k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6) = c4_65_2__funct_6 )
    & ( c1_65_2_2__funct_6 != c2_65_2__funct_6
     => k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6) = k1_funct_1(c3_65__funct_6,c1_65_2_2__funct_6) )
    & r2_hidden(k1_funct_1(c3_65__funct_6,c1_65_2_2__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_2__funct_6))
    & ~ ( c1_65_2_2__funct_6 != c2_65_2__funct_6
        & c1_65_2_2__funct_6 = c2_65_2__funct_6 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_65_2_2__funct_6,e1_65_2_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k7_funct_6,dt_c1_65__funct_6,dt_c1_65_2_2__funct_6,dt_c2_65__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c4_65_2__funct_6,dt_c6_65_2__funct_6,t1_subset,t7_boole,e1_65_2_2__funct_6,e6_65__funct_6,e7_65__funct_6,e11_65_2__funct_6]),
    [interesting(0.5),file(funct_6,e2_65_2_2__funct_6),[file(funct_6,e2_65_2_2__funct_6)]]).

fof(e3_65_2_2__funct_6,plain,(
    r2_hidden(k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_2__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_65_2__funct_6,dt_c1_65_2_2__funct_6,e1_65_2_2__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k3_funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,dt_c1_65_2_2__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c3_65_2__funct_6,dt_c4_65_2__funct_6,dt_c6_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,e2_65_2_2__funct_6,e4_65_2__funct_6,e12_65_2__funct_6,t31_funct_6]),
    [interesting(0.5),file(funct_6,e3_65_2_2__funct_6),[file(funct_6,e3_65_2_2__funct_6)]]).

fof(i3_65_2_2__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_65_2_2__funct_6)]),
    [interesting(0.5),trivial,file(funct_6,i3_65_2_2__funct_6)]).

fof(i2_65_2_2__funct_6,plain,(
    r2_hidden(k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_2__funct_6)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_65_2__funct_6,dt_c1_65_2_2__funct_6,e1_65_2_2__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6])],[e3_65_2_2__funct_6,i3_65_2_2__funct_6]),
    [interesting(0.5),file(funct_6,i2_65_2_2__funct_6),[file(funct_6,i2_65_2_2__funct_6)]]).

fof(i1_65_2_2__funct_6,plain,
    ( r2_hidden(c1_65_2_2__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
   => r2_hidden(k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_2__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_65_2__funct_6,dt_c1_65_2_2__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6]),discharge_asm(discharge,[e1_65_2_2__funct_6])],[e1_65_2_2__funct_6,i2_65_2_2__funct_6]),
    [interesting(0.5),file(funct_6,i1_65_2_2__funct_6),[file(funct_6,i1_65_2_2__funct_6)]]).

fof(i1_65_2_2_tmp__funct_6,plain,
    ( r2_hidden(c1_65_2_2__funct_6,k1_relat_1(k2_funct_6(c1_65__funct_6)))
   => r2_hidden(k1_funct_1(c6_65_2__funct_6,c1_65_2_2__funct_6),k1_funct_1(k2_funct_6(c1_65__funct_6),c1_65_2_2__funct_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_65_2__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6]),discharge_asm(discharge,[dt_c1_65_2_2__funct_6])],[dt_c1_65_2_2__funct_6,i1_65_2_2__funct_6]),
    [interesting(0.65),e17_65_2__funct_6]).

fof(e17_65_2__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k2_funct_6(c1_65__funct_6)))
     => r2_hidden(k1_funct_1(c6_65_2__funct_6,A),k1_funct_1(k2_funct_6(c1_65__funct_6),A)) ) ),
    inference(let,[status(thm),assumptions([dt_c3_65_2__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6,dt_c1_65__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,e12_65_2__funct_6])],[i1_65_2_2_tmp__funct_6,dh_c1_65_2_2__funct_6]),
    [interesting(0.65),file(funct_6,e17_65_2__funct_6),[file(funct_6,e17_65_2__funct_6)]]).

fof(e18_65_2__funct_6,plain,(
    r2_hidden(c6_65_2__funct_6,k4_card_3(k2_funct_6(c1_65__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_65_2__funct_6,e12_65_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k7_funct_6,dt_c1_65__funct_6,dt_c2_65_2__funct_6,dt_c3_65__funct_6,dt_c4_65_2__funct_6,dt_c6_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,e17_65_2__funct_6,e7_65__funct_6,e11_65_2__funct_6,d5_card_3]),
    [interesting(0.65),file(funct_6,e18_65_2__funct_6),[file(funct_6,e18_65_2__funct_6)]]).

fof(e19_65_2__funct_6,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_funct_1(k7_funct_6(c1_65__funct_6),c6_65_2__funct_6) = A
      & k1_relat_1(A) = k10_relat_1(c1_65__funct_6,k1_funct_6(k2_relat_1(c1_65__funct_6)))
      & ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k1_funct_1(A,B) = k1_funct_1(k4_funct_5(c1_65__funct_6),k4_tarski(B,k1_funct_1(c6_65_2__funct_6,B))) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_65_2__funct_6,e12_65_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[cc1_finseq_1,fc11_finseq_1,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,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,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_6,dt_k1_relat_1,dt_k2_funct_6,dt_k2_relat_1,dt_k4_card_3,dt_k4_funct_5,dt_k4_tarski,dt_k7_funct_6,dt_c1_65__funct_6,dt_c6_65_2__funct_6,rc1_funct_1,t1_subset,t7_boole,d5_tarski,e18_65_2__funct_6,d7_funct_6]),
    [interesting(0.65),file(funct_6,e19_65_2__funct_6),[file(funct_6,e19_65_2__funct_6)]]).

fof(dt_c8_65_2__funct_6,plain,
    ( v1_relat_1(c8_65_2__funct_6)
    & v1_funct_1(c8_65_2__funct_6) ),
    inference(consider,[status(thm),assumptions([dt_c3_65_2__funct_6,e12_65_2__funct_6,dt_c1_65_2__funct_6,e2_65_2__funct_6,dt_c1_65__funct_6,e1_65__funct_6,dt_c4_65_2__funct_6])],[dh_c8_65_2__funct_6,e19_65_2__funct_6]),
    [interesting(0.65),file(funct_6,c8_65_2__funct_6),[file(funct_6,c8_65_2__funct_6)]]).
ERROR: Line 283 Char 6 Token "ERROR" continuing with " Line 1184 Char 6 T"