% Mizar ND problem: t29_funct_6,funct_6,621,29 
fof(dh_c1_31__funct_6,definition,
    ( ( ( v1_relat_1(c1_31__funct_6)
        & v1_funct_1(c1_31__funct_6) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
                & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
                & k1_funct_6(k2_tarski(c1_31__funct_6,A)) = k2_tarski(c1_31__funct_6,A)
                & k1_funct_6(k1_enumset1(c1_31__funct_6,A,B)) = k1_enumset1(c1_31__funct_6,A,B) ) ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D) )
           => ! [E] : 
                ( ( v1_relat_1(E)
                  & v1_funct_1(E) )
               => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
                  & k1_funct_6(k1_tarski(C)) = k1_tarski(C)
                  & k1_funct_6(k2_tarski(C,D)) = k2_tarski(C,D)
                  & k1_funct_6(k1_enumset1(C,D,E)) = k1_enumset1(C,D,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_31__funct_6),file(funct_6,c1_31__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_31__funct_6)]).

fof(dh_c2_31__funct_6,definition,
    ( ( ( v1_relat_1(c2_31__funct_6)
        & v1_funct_1(c2_31__funct_6) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
            & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
            & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
            & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,A)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,A) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
              & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
              & k1_funct_6(k2_tarski(c1_31__funct_6,B)) = k2_tarski(c1_31__funct_6,B)
              & k1_funct_6(k1_enumset1(c1_31__funct_6,B,C)) = k1_enumset1(c1_31__funct_6,B,C) ) ) ) ),
    introduced(definition,[new_symbol(c2_31__funct_6),file(funct_6,c2_31__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_31__funct_6)]).

fof(dh_c3_31__funct_6,definition,
    ( ( ( v1_relat_1(c3_31__funct_6)
        & v1_funct_1(c3_31__funct_6) )
     => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
        & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
        & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
        & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
          & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
          & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
          & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,A)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,A) ) ) ),
    introduced(definition,[new_symbol(c3_31__funct_6),file(funct_6,c3_31__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_31__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(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(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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_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(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(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_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(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(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_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_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(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_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_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(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(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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

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

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(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_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(t27_funct_6,theorem,(
    ! [A] : r1_tarski(k1_funct_6(A),A) ),
    file(funct_6,t27_funct_6),
    [interesting(0.9),axiom,file(funct_6,t27_funct_6)]).

fof(e1_31__funct_6,plain,(
    r1_tarski(k1_funct_6(k1_xboole_0),k1_xboole_0) ),
    inference(mizar_by,[status(thm),assumptions([])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_subset_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_funct_6,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,t3_subset,t6_boole,t27_funct_6]),
    [interesting(0.8),file(funct_6,e1_31__funct_6),[file(funct_6,e1_31__funct_6)]]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]).

fof(e2_31__funct_6,plain,(
    k1_funct_6(k1_xboole_0) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_subset_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_funct_6,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,t3_subset,t6_boole,e1_31__funct_6,t3_xboole_1]),
    [interesting(0.8),file(funct_6,e2_31__funct_6),[file(funct_6,e2_31__funct_6)]]).

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

fof(dt_c1_31__funct_6,assumption,
    ( v1_relat_1(c1_31__funct_6)
    & v1_funct_1(c1_31__funct_6) ),
    introduced(assumption,[file(funct_6,c1_31__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_31__funct_6)]).

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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e3_31__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_tarski(c1_31__funct_6))
     => ( v1_relat_1(A)
        & v1_funct_1(A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_31__funct_6])],[cc1_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,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_c1_31__funct_6,fc2_subset_1,rc1_funct_1,t1_subset,t7_boole,d1_tarski]),
    [interesting(0.8),file(funct_6,e3_31__funct_6),[file(funct_6,e3_31__funct_6)]]).

fof(l30_funct_6,plain,(
    ! [A] : 
      ( ! [B] : 
          ( r2_hidden(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) )
     => k1_funct_6(A) = A ) ),
    file(funct_6,l30_funct_6),
    [interesting(0.9),axiom,file(funct_6,l30_funct_6)]).

fof(e4_31__funct_6,plain,(
    k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_31__funct_6])],[cc1_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,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_6,dt_k1_tarski,dt_c1_31__funct_6,fc2_subset_1,rc1_funct_1,t1_subset,t7_boole,e3_31__funct_6,l30_funct_6]),
    [interesting(0.8),file(funct_6,e4_31__funct_6),[file(funct_6,e4_31__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_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_c2_31__funct_6,assumption,
    ( v1_relat_1(c2_31__funct_6)
    & v1_funct_1(c2_31__funct_6) ),
    introduced(assumption,[file(funct_6,c2_31__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c2_31__funct_6)]).

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(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.9),axiom,file(tarski,d2_tarski)]).

fof(e5_31__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_tarski(c1_31__funct_6,c2_31__funct_6))
     => ( v1_relat_1(A)
        & v1_funct_1(A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6])],[cc1_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,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_tarski,dt_c1_31__funct_6,dt_c2_31__funct_6,fc3_subset_1,rc1_funct_1,t1_subset,t7_boole,d2_tarski]),
    [interesting(0.8),file(funct_6,e5_31__funct_6),[file(funct_6,e5_31__funct_6)]]).

fof(e6_31__funct_6,plain,(
    k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6])],[cc1_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,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_6,dt_k2_tarski,dt_c1_31__funct_6,dt_c2_31__funct_6,fc3_subset_1,rc1_funct_1,t1_subset,t7_boole,e5_31__funct_6,l30_funct_6]),
    [interesting(0.8),file(funct_6,e6_31__funct_6),[file(funct_6,e6_31__funct_6)]]).

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    [interesting(0.9),axiom,file(enumset1,k1_enumset1)]).

fof(dt_c3_31__funct_6,assumption,
    ( v1_relat_1(c3_31__funct_6)
    & v1_funct_1(c3_31__funct_6) ),
    introduced(assumption,[file(funct_6,c3_31__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c3_31__funct_6)]).

fof(d1_enumset1,definition,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    [interesting(0.9),axiom,file(enumset1,d1_enumset1)]).

fof(e7_31__funct_6,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6))
     => ( v1_relat_1(A)
        & v1_funct_1(A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6])],[cc1_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,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_enumset1,dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6,rc1_funct_1,t1_subset,t7_boole,d1_enumset1]),
    [interesting(0.8),file(funct_6,e7_31__funct_6),[file(funct_6,e7_31__funct_6)]]).

fof(e8_31__funct_6,plain,(
    k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6])],[cc1_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,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_enumset1,dt_k1_funct_6,dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6,rc1_funct_1,t1_subset,t7_boole,e7_31__funct_6,l30_funct_6]),
    [interesting(0.8),file(funct_6,e8_31__funct_6),[file(funct_6,e8_31__funct_6)]]).

fof(i7_31__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i7_31__funct_6)]),
    [interesting(0.8),trivial,file(funct_6,i7_31__funct_6)]).

fof(i6_31__funct_6,plain,(
    k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6])],[e8_31__funct_6,i7_31__funct_6]),
    [interesting(0.8),file(funct_6,i6_31__funct_6),[file(funct_6,i6_31__funct_6)]]).

fof(i5_31__funct_6,plain,
    ( k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
    & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6])],[e6_31__funct_6,i6_31__funct_6]),
    [interesting(0.8),file(funct_6,i5_31__funct_6),[file(funct_6,i5_31__funct_6)]]).

fof(i4_31__funct_6,plain,
    ( k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
    & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
    & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6])],[e4_31__funct_6,i5_31__funct_6]),
    [interesting(0.8),file(funct_6,i4_31__funct_6),[file(funct_6,i4_31__funct_6)]]).

fof(i3_31__funct_6,plain,
    ( k1_funct_6(k1_xboole_0) = k1_xboole_0
    & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
    & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
    & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6,dt_c3_31__funct_6])],[e2_31__funct_6,i4_31__funct_6]),
    [interesting(0.8),file(funct_6,i3_31__funct_6),[file(funct_6,i3_31__funct_6)]]).

fof(i3_31_tmp__funct_6,plain,
    ( ( v1_relat_1(c3_31__funct_6)
      & v1_funct_1(c3_31__funct_6) )
   => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
      & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
      & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
      & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,c3_31__funct_6) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6]),discharge_asm(discharge,[dt_c3_31__funct_6])],[dt_c3_31__funct_6,i3_31__funct_6]),
    [interesting(0.8),i2_31__funct_6]).

fof(i2_31__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
        & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
        & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
        & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,A)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_31__funct_6,dt_c2_31__funct_6])],[i3_31_tmp__funct_6,dh_c3_31__funct_6]),
    [interesting(0.8),file(funct_6,i2_31__funct_6),[file(funct_6,i2_31__funct_6)]]).

fof(i2_31_tmp__funct_6,plain,
    ( ( v1_relat_1(c2_31__funct_6)
      & v1_funct_1(c2_31__funct_6) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
          & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
          & k1_funct_6(k2_tarski(c1_31__funct_6,c2_31__funct_6)) = k2_tarski(c1_31__funct_6,c2_31__funct_6)
          & k1_funct_6(k1_enumset1(c1_31__funct_6,c2_31__funct_6,A)) = k1_enumset1(c1_31__funct_6,c2_31__funct_6,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_31__funct_6]),discharge_asm(discharge,[dt_c2_31__funct_6])],[dt_c2_31__funct_6,i2_31__funct_6]),
    [interesting(0.8),i1_31__funct_6]).

fof(i1_31__funct_6,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
            & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
            & k1_funct_6(k2_tarski(c1_31__funct_6,A)) = k2_tarski(c1_31__funct_6,A)
            & k1_funct_6(k1_enumset1(c1_31__funct_6,A,B)) = k1_enumset1(c1_31__funct_6,A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_31__funct_6])],[i2_31_tmp__funct_6,dh_c2_31__funct_6]),
    [interesting(0.8),file(funct_6,i1_31__funct_6),[file(funct_6,i1_31__funct_6)]]).

fof(i1_31_tmp__funct_6,plain,
    ( ( v1_relat_1(c1_31__funct_6)
      & v1_funct_1(c1_31__funct_6) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
              & k1_funct_6(k1_tarski(c1_31__funct_6)) = k1_tarski(c1_31__funct_6)
              & k1_funct_6(k2_tarski(c1_31__funct_6,A)) = k2_tarski(c1_31__funct_6,A)
              & k1_funct_6(k1_enumset1(c1_31__funct_6,A,B)) = k1_enumset1(c1_31__funct_6,A,B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_31__funct_6])],[dt_c1_31__funct_6,i1_31__funct_6]),
    [interesting(1),t29_funct_6]).

fof(t29_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( k1_funct_6(k1_xboole_0) = k1_xboole_0
                & k1_funct_6(k1_tarski(A)) = k1_tarski(A)
                & k1_funct_6(k2_tarski(A,B)) = k2_tarski(A,B)
                & k1_funct_6(k1_enumset1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_31_tmp__funct_6,dh_c1_31__funct_6]),
    [interesting(1),file(funct_6,t29_funct_6),[file(funct_6,t29_funct_6)]]).