% Mizar ND problem: t1_trees_1,trees_1,35,55 
fof(dh_c1_1__trees_1,definition,
    ( ( m2_subset_1(c1_1__trees_1,k1_numbers,k5_numbers)
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A)
            & v1_finseq_1(A) )
         => ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ( B = k7_relat_1(A,k2_finseq_1(c1_1__trees_1))
               => r1_xreal_0(k3_finseq_1(B),c1_1__trees_1) ) ) ) )
   => ! [C] : 
        ( m2_subset_1(C,k1_numbers,k5_numbers)
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D)
              & v1_finseq_1(D) )
           => ! [E] : 
                ( ( v1_relat_1(E)
                  & v1_funct_1(E)
                  & v1_finseq_1(E) )
               => ( E = k7_relat_1(D,k2_finseq_1(C))
                 => r1_xreal_0(k3_finseq_1(E),C) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__trees_1),file(trees_1,c1_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c1_1__trees_1)]).

fof(dh_c2_1__trees_1,definition,
    ( ( ( v1_relat_1(c2_1__trees_1)
        & v1_funct_1(c2_1__trees_1)
        & v1_finseq_1(c2_1__trees_1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A)
            & v1_finseq_1(A) )
         => ( A = k7_relat_1(c2_1__trees_1,k2_finseq_1(c1_1__trees_1))
           => r1_xreal_0(k3_finseq_1(A),c1_1__trees_1) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finseq_1(C) )
           => ( C = k7_relat_1(B,k2_finseq_1(c1_1__trees_1))
             => r1_xreal_0(k3_finseq_1(C),c1_1__trees_1) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__trees_1),file(trees_1,c2_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c2_1__trees_1)]).

fof(dh_c3_1__trees_1,definition,
    ( ( ( v1_relat_1(c3_1__trees_1)
        & v1_funct_1(c3_1__trees_1)
        & v1_finseq_1(c3_1__trees_1) )
     => ( c3_1__trees_1 = k7_relat_1(c2_1__trees_1,k2_finseq_1(c1_1__trees_1))
       => r1_xreal_0(k3_finseq_1(c3_1__trees_1),c1_1__trees_1) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => ( A = k7_relat_1(c2_1__trees_1,k2_finseq_1(c1_1__trees_1))
         => r1_xreal_0(k3_finseq_1(A),c1_1__trees_1) ) ) ),
    introduced(definition,[new_symbol(c3_1__trees_1),file(trees_1,c3_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c3_1__trees_1)]).

fof(e1_1__trees_1,assumption,(
    c3_1__trees_1 = k7_relat_1(c2_1__trees_1,k2_finseq_1(c1_1__trees_1)) ),
    introduced(assumption,[file(trees_1,e1_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,e1_1__trees_1)]).

fof(rc2_finset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc2_finset_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(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(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

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

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

fof(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(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(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_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_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_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(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc3_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

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(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

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(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(t5_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

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(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

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(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

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(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

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(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

fof(dt_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

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_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

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

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_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_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

fof(cc2_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(fc1_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc1_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(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(redefinition_k2_finseq_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(redefinition_k3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

fof(dt_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

fof(dt_c1_1__trees_1,assumption,(
    m2_subset_1(c1_1__trees_1,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(trees_1,c1_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c1_1__trees_1)]).

fof(dt_c3_1__trees_1,assumption,
    ( v1_relat_1(c3_1__trees_1)
    & v1_funct_1(c3_1__trees_1)
    & v1_finseq_1(c3_1__trees_1) ),
    introduced(assumption,[file(trees_1,c3_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c3_1__trees_1)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_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(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

fof(fc10_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc10_finset_1)]).

fof(fc11_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc11_finset_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(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(commutativity_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(idempotence_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(redefinition_k4_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

fof(redefinition_k5_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(dt_c2_1__trees_1,assumption,
    ( v1_relat_1(c2_1__trees_1)
    & v1_funct_1(c2_1__trees_1)
    & v1_finseq_1(c2_1__trees_1) ),
    introduced(assumption,[file(trees_1,c2_1__trees_1)]),
    [interesting(0.8),axiom,file(trees_1,c2_1__trees_1)]).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    [interesting(0.9),axiom,file(relat_1,k7_relat_1)]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,d3_finseq_1)]).

fof(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    [interesting(0.9),axiom,file(relat_1,t90_relat_1)]).

fof(e2_1__trees_1,plain,
    ( k4_finseq_1(c3_1__trees_1) = k5_subset_1(k5_numbers,k4_finseq_1(c2_1__trees_1),k2_finseq_1(c1_1__trees_1))
    & k2_finseq_1(k3_finseq_1(c3_1__trees_1)) = k4_finseq_1(c3_1__trees_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1,e1_1__trees_1])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_xboole_0,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc3_nat_1,t1_subset,t2_boole,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc3_nat_1,fc10_finset_1,fc11_finset_1,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k5_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k3_xboole_0,dt_k4_finseq_1,dt_k5_numbers,dt_k5_subset_1,dt_k7_relat_1,dt_m2_subset_1,dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1,cc1_finseq_1,rc1_finseq_1,e1_1__trees_1,d3_finseq_1,t90_relat_1]),
    [interesting(0.8),file(trees_1,e2_1__trees_1),[file(trees_1,e2_1__trees_1)]]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t17_xboole_1)]).

fof(e3_1__trees_1,plain,(
    r1_tarski(k2_finseq_1(k3_finseq_1(c3_1__trees_1)),k2_finseq_1(c1_1__trees_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1,e1_1__trees_1])],[rc2_finset_1,rc3_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_boole,t4_subset,t5_subset,cc1_finset_1,cc2_finset_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc10_finset_1,fc11_finset_1,fc17_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xboole_0,rc1_xreal_0,rc2_nat_1,rc2_xboole_0,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_nat_1,cc1_xreal_0,cc2_nat_1,cc3_nat_1,fc1_finseq_1,fc1_ordinal2,rc1_finseq_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,reflexivity_r1_tarski,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k5_subset_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k3_xboole_0,dt_k4_finseq_1,dt_k5_numbers,dt_k5_subset_1,dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1,t3_subset,e2_1__trees_1,t17_xboole_1]),
    [interesting(0.8),file(trees_1,e3_1__trees_1),[file(trees_1,e3_1__trees_1)]]).

fof(t7_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
          <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ),
    file(finseq_1,t7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t7_finseq_1)]).

fof(e4_1__trees_1,plain,(
    r1_xreal_0(k3_finseq_1(c3_1__trees_1),c1_1__trees_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1,e1_1__trees_1])],[rc2_finset_1,rc3_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,dt_k5_ordinal2,cc1_finset_1,cc2_finset_1,cc3_xreal_0,cc4_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_finset_1,rc1_nat_1,rc1_xboole_0,rc2_nat_1,rc2_xboole_0,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_real,t2_subset,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_finseq_1,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc5_xreal_0,fc1_finseq_1,rc1_finseq_1,rc1_xreal_0,t2_real,t3_real,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_c1_1__trees_1,dt_c3_1__trees_1,cc1_xreal_0,cc3_nat_1,t3_subset,e3_1__trees_1,t7_finseq_1]),
    [interesting(0.8),file(trees_1,e4_1__trees_1),[file(trees_1,e4_1__trees_1)]]).

fof(i4_1__trees_1,theorem,(
    $true ),
    introduced(tautology,[file(trees_1,i4_1__trees_1)]),
    [interesting(0.8),trivial,file(trees_1,i4_1__trees_1)]).

fof(i3_1__trees_1,plain,(
    r1_xreal_0(k3_finseq_1(c3_1__trees_1),c1_1__trees_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1,e1_1__trees_1])],[e4_1__trees_1,i4_1__trees_1]),
    [interesting(0.8),file(trees_1,i3_1__trees_1),[file(trees_1,i3_1__trees_1)]]).

fof(i2_1__trees_1,plain,
    ( c3_1__trees_1 = k7_relat_1(c2_1__trees_1,k2_finseq_1(c1_1__trees_1))
   => r1_xreal_0(k3_finseq_1(c3_1__trees_1),c1_1__trees_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__trees_1,dt_c2_1__trees_1,dt_c3_1__trees_1]),discharge_asm(discharge,[e1_1__trees_1])],[e1_1__trees_1,i3_1__trees_1]),
    [interesting(0.8),file(trees_1,i2_1__trees_1),[file(trees_1,i2_1__trees_1)]]).

fof(i2_1_tmp__trees_1,plain,
    ( ( v1_relat_1(c2_1__trees_1)
      & v1_funct_1(c2_1__trees_1)
      & v1_finseq_1(c2_1__trees_1)
      & v1_relat_1(c3_1__trees_1)
      & v1_funct_1(c3_1__trees_1)
      & v1_finseq_1(c3_1__trees_1) )
   => ( c3_1__trees_1 = k7_relat_1(c2_1__trees_1,k2_finseq_1(c1_1__trees_1))
     => r1_xreal_0(k3_finseq_1(c3_1__trees_1),c1_1__trees_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__trees_1]),discharge_asm(discharge,[dt_c2_1__trees_1,dt_c3_1__trees_1])],[dt_c2_1__trees_1,dt_c3_1__trees_1,i2_1__trees_1]),
    [interesting(0.8),i1_1__trees_1]).

fof(i1_1__trees_1,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( B = k7_relat_1(A,k2_finseq_1(c1_1__trees_1))
           => r1_xreal_0(k3_finseq_1(B),c1_1__trees_1) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__trees_1])],[i2_1_tmp__trees_1,dh_c2_1__trees_1,dh_c3_1__trees_1]),
    [interesting(0.8),file(trees_1,i1_1__trees_1),[file(trees_1,i1_1__trees_1)]]).

fof(i1_1_tmp__trees_1,plain,
    ( m2_subset_1(c1_1__trees_1,k1_numbers,k5_numbers)
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) )
           => ( B = k7_relat_1(A,k2_finseq_1(c1_1__trees_1))
             => r1_xreal_0(k3_finseq_1(B),c1_1__trees_1) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__trees_1])],[dt_c1_1__trees_1,i1_1__trees_1]),
    [interesting(1),t1_trees_1]).

fof(t1_trees_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( C = k7_relat_1(B,k2_finseq_1(A))
               => r1_xreal_0(k3_finseq_1(C),A) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__trees_1,dh_c1_1__trees_1]),
    [interesting(1),file(trees_1,t1_trees_1),[file(trees_1,t1_trees_1)]]).