% Mizar ND problem: t7_trees_2,trees_2,145,52 
fof(dh_c1_7__trees_2,definition,
    ( ( ( ~ v1_xboole_0(c1_7__trees_2)
        & v1_trees_1(c1_7__trees_2) )
     => ! [A] : 
          ( ( ~ v1_xboole_0(A)
            & v1_trees_1(A) )
         => ( ! [B] : 
                ( m2_finseq_1(B,k5_numbers)
               => ( r2_hidden(B,c1_7__trees_2)
                <=> r2_hidden(B,A) ) )
           => c1_7__trees_2 = A ) ) )
   => ! [C] : 
        ( ( ~ v1_xboole_0(C)
          & v1_trees_1(C) )
       => ! [D] : 
            ( ( ~ v1_xboole_0(D)
              & v1_trees_1(D) )
           => ( ! [E] : 
                  ( m2_finseq_1(E,k5_numbers)
                 => ( r2_hidden(E,C)
                  <=> r2_hidden(E,D) ) )
             => C = D ) ) ) ),
    introduced(definition,[new_symbol(c1_7__trees_2),file(trees_2,c1_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c1_7__trees_2)]).

fof(dh_c2_7__trees_2,definition,
    ( ( ( ~ v1_xboole_0(c2_7__trees_2)
        & v1_trees_1(c2_7__trees_2) )
     => ( ! [A] : 
            ( m2_finseq_1(A,k5_numbers)
           => ( r2_hidden(A,c1_7__trees_2)
            <=> r2_hidden(A,c2_7__trees_2) ) )
       => c1_7__trees_2 = c2_7__trees_2 ) )
   => ! [B] : 
        ( ( ~ v1_xboole_0(B)
          & v1_trees_1(B) )
       => ( ! [C] : 
              ( m2_finseq_1(C,k5_numbers)
             => ( r2_hidden(C,c1_7__trees_2)
              <=> r2_hidden(C,B) ) )
         => c1_7__trees_2 = B ) ) ),
    introduced(definition,[new_symbol(c2_7__trees_2),file(trees_2,c2_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c2_7__trees_2)]).

fof(e1_7__trees_2,assumption,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ( r2_hidden(A,c1_7__trees_2)
      <=> r2_hidden(A,c2_7__trees_2) ) ) ),
    introduced(assumption,[file(trees_2,e1_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,e1_7__trees_2)]).

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_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_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_trees_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_1(A) ) ),
    file(trees_1,rc2_trees_1),
    [interesting(0.9),axiom,file(trees_1,rc2_trees_1)]).

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(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(rc1_trees_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_trees_1(A) ) ),
    file(trees_1,rc1_trees_1),
    [interesting(0.9),axiom,file(trees_1,rc1_trees_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_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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_c1_7__trees_2,assumption,
    ( ~ v1_xboole_0(c1_7__trees_2)
    & v1_trees_1(c1_7__trees_2) ),
    introduced(assumption,[file(trees_2,c1_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c1_7__trees_2)]).

fof(dt_c2_7__trees_2,assumption,
    ( ~ v1_xboole_0(c2_7__trees_2)
    & v1_trees_1(c2_7__trees_2) ),
    introduced(assumption,[file(trees_2,c2_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c2_7__trees_2)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

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_c1_7_1__trees_2,assumption,(
    $true ),
    introduced(assumption,[file(trees_2,c1_7_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_7_1__trees_2)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_7_1__trees_2,definition,
    ( ~ ( r2_hidden(c1_7_1__trees_2,c1_7__trees_2)
        & ~ r2_hidden(c1_7_1__trees_2,c2_7__trees_2) )
   => ! [A] : 
        ~ ( r2_hidden(A,c1_7__trees_2)
          & ~ r2_hidden(A,c2_7__trees_2) ) ),
    introduced(definition,[new_symbol(c1_7_1__trees_2),file(trees_2,c1_7_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_7_1__trees_2)]).

fof(e1_7_1__trees_2,assumption,(
    r2_hidden(c1_7_1__trees_2,c1_7__trees_2) ),
    introduced(assumption,[file(trees_2,e1_7_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,e1_7_1__trees_2)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_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(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(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(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]).

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

fof(rc2_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]).

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_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_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(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_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_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_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_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(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(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(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(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(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(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(fc1_numbers,theorem,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    [interesting(0.9),axiom,file(numbers,fc1_numbers)]).

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(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_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_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(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(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(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_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_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_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_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]).

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(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(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(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_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_finseq_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_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(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_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_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(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

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

fof(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(existence_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : m1_trees_1(B,A) ) ),
    file(trees_1,m1_trees_1),
    [interesting(0.9),axiom,file(trees_1,m1_trees_1)]).

fof(redefinition_m1_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
        <=> m1_subset_1(B,A) ) ) ),
    file(trees_1,m1_trees_1),
    [interesting(0.9),axiom,file(trees_1,m1_trees_1)]).

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

fof(dt_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => m2_finseq_1(B,k5_numbers) ) ) ),
    file(trees_1,m1_trees_1),
    [interesting(0.9),axiom,file(trees_1,m1_trees_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(de_c2_7_1__trees_2,definition,(
    c2_7_1__trees_2 = c1_7_1__trees_2 ),
    introduced(definition,[new_symbol(c2_7_1__trees_2),file(trees_2,c2_7_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c2_7_1__trees_2)]).

fof(e2_7_1__trees_2,plain,(
    m1_trees_1(c1_7_1__trees_2,c1_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__trees_2,dt_c1_7_1__trees_2,e1_7_1__trees_2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_nat_1,cc1_relat_1,cc2_nat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_trees_1,dt_c1_7__trees_2,dt_c1_7_1__trees_2,t1_subset,t7_boole,e1_7_1__trees_2]),
    [interesting(0.65),file(trees_2,e2_7_1__trees_2),[file(trees_2,e2_7_1__trees_2)]]).

fof(dt_c2_7_1__trees_2,plain,(
    m1_trees_1(c2_7_1__trees_2,c1_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__trees_2,dt_c1_7_1__trees_2,e1_7_1__trees_2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_nat_1,cc1_relat_1,cc2_nat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_trees_1,dt_c1_7__trees_2,dt_c1_7_1__trees_2,de_c2_7_1__trees_2,e2_7_1__trees_2]),
    [interesting(0.65),file(trees_2,c2_7_1__trees_2),[file(trees_2,c2_7_1__trees_2)]]).

fof(e3_7_1__trees_2,plain,(
    r2_hidden(c2_7_1__trees_2,c2_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__trees_2,dt_c1_7__trees_2,dt_c1_7_1__trees_2,e1_7_1__trees_2,e1_7__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_relat_1,rc2_trees_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_relset_1,redefinition_m1_trees_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_relset_1,dt_c1_7_1__trees_2,cc1_finset_1,cc1_nat_1,cc1_relat_1,cc2_nat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_subset_1,rc1_trees_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_c1_7__trees_2,dt_c2_7__trees_2,dt_c2_7_1__trees_2,de_c2_7_1__trees_2,t1_subset,t7_boole,e1_7__trees_2]),
    [interesting(0.65),file(trees_2,e3_7_1__trees_2),[file(trees_2,e3_7_1__trees_2)]]).

fof(e4_7_1__trees_2,plain,(
    r2_hidden(c1_7_1__trees_2,c2_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__trees_2,dt_c1_7__trees_2,dt_c1_7_1__trees_2,e1_7_1__trees_2,e1_7__trees_2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_finseq_1,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_numbers,dt_m2_finseq_1,cc1_nat_1,cc2_nat_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc2_trees_1,existence_m1_subset_1,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_subset_1,dt_m1_trees_1,dt_c1_7__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_c1_7_1__trees_2,dt_c2_7__trees_2,dt_c2_7_1__trees_2,de_c2_7_1__trees_2,t1_subset,t7_boole,e3_7_1__trees_2]),
    [interesting(0.65),file(trees_2,e4_7_1__trees_2),[file(trees_2,e4_7_1__trees_2)]]).

fof(i3_7_1__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i3_7_1__trees_2)]),
    [interesting(0.65),trivial,file(trees_2,i3_7_1__trees_2)]).

fof(i2_7_1__trees_2,plain,(
    r2_hidden(c1_7_1__trees_2,c2_7__trees_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_7__trees_2,dt_c1_7__trees_2,dt_c1_7_1__trees_2,e1_7_1__trees_2,e1_7__trees_2])],[e4_7_1__trees_2,i3_7_1__trees_2]),
    [interesting(0.65),file(trees_2,i2_7_1__trees_2),[file(trees_2,i2_7_1__trees_2)]]).

fof(i1_7_1__trees_2,plain,(
    ~ ( r2_hidden(c1_7_1__trees_2,c1_7__trees_2)
      & ~ r2_hidden(c1_7_1__trees_2,c2_7__trees_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_7__trees_2,dt_c1_7__trees_2,dt_c1_7_1__trees_2,e1_7__trees_2]),discharge_asm(discharge,[e1_7_1__trees_2])],[e1_7_1__trees_2,i2_7_1__trees_2]),
    [interesting(0.65),file(trees_2,i1_7_1__trees_2),[file(trees_2,i1_7_1__trees_2)]]).

fof(i1_7_1_tmp__trees_2,plain,(
    ~ ( r2_hidden(c1_7_1__trees_2,c1_7__trees_2)
      & ~ r2_hidden(c1_7_1__trees_2,c2_7__trees_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_7__trees_2,dt_c1_7__trees_2,e1_7__trees_2]),discharge_asm(discharge,[dt_c1_7_1__trees_2])],[dt_c1_7_1__trees_2,i1_7_1__trees_2]),
    [interesting(0.8),e2_7__trees_2]).

fof(e2_7__trees_2,plain,(
    r1_tarski(c1_7__trees_2,c2_7__trees_2) ),
    inference(let,[status(thm),assumptions([dt_c2_7__trees_2,dt_c1_7__trees_2,e1_7__trees_2])],[i1_7_1_tmp__trees_2,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc2_trees_1,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_7__trees_2,dt_c2_7__trees_2,d3_tarski,dh_c1_7_1__trees_2]),
    [interesting(0.8),file(trees_2,e2_7__trees_2),[file(trees_2,e2_7__trees_2)]]).

fof(dt_c3_7__trees_2,assumption,(
    $true ),
    introduced(assumption,[file(trees_2,c3_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c3_7__trees_2)]).

fof(dh_c3_7__trees_2,definition,
    ( ~ ( r2_hidden(c3_7__trees_2,c2_7__trees_2)
        & ~ r2_hidden(c3_7__trees_2,c1_7__trees_2) )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_7__trees_2)
          & ~ r2_hidden(A,c1_7__trees_2) ) ),
    introduced(definition,[new_symbol(c3_7__trees_2),file(trees_2,c3_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c3_7__trees_2)]).

fof(e3_7__trees_2,assumption,(
    r2_hidden(c3_7__trees_2,c2_7__trees_2) ),
    introduced(assumption,[file(trees_2,e3_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,e3_7__trees_2)]).

fof(de_c4_7__trees_2,definition,(
    c4_7__trees_2 = c3_7__trees_2 ),
    introduced(definition,[new_symbol(c4_7__trees_2),file(trees_2,c4_7__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c4_7__trees_2)]).

fof(e4_7__trees_2,plain,(
    m1_trees_1(c3_7__trees_2,c2_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__trees_2,dt_c3_7__trees_2,e3_7__trees_2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_nat_1,cc1_relat_1,cc2_nat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_trees_1,dt_c2_7__trees_2,dt_c3_7__trees_2,t1_subset,t7_boole,e3_7__trees_2]),
    [interesting(0.8),file(trees_2,e4_7__trees_2),[file(trees_2,e4_7__trees_2)]]).

fof(dt_c4_7__trees_2,plain,(
    m1_trees_1(c4_7__trees_2,c2_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__trees_2,dt_c3_7__trees_2,e3_7__trees_2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_nat_1,cc1_relat_1,cc2_nat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_trees_1,dt_c2_7__trees_2,dt_c3_7__trees_2,de_c4_7__trees_2,e4_7__trees_2]),
    [interesting(0.8),file(trees_2,c4_7__trees_2),[file(trees_2,c4_7__trees_2)]]).

fof(e5_7__trees_2,plain,(
    r2_hidden(c4_7__trees_2,c1_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,dt_c3_7__trees_2,e3_7__trees_2,e1_7__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_relat_1,rc2_trees_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_relset_1,redefinition_m1_trees_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_relset_1,dt_c3_7__trees_2,cc1_finset_1,cc1_nat_1,cc1_relat_1,cc2_nat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_subset_1,rc1_trees_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_c1_7__trees_2,dt_c2_7__trees_2,dt_c4_7__trees_2,de_c4_7__trees_2,t1_subset,t7_boole,e1_7__trees_2]),
    [interesting(0.8),file(trees_2,e5_7__trees_2),[file(trees_2,e5_7__trees_2)]]).

fof(e6_7__trees_2,plain,(
    r2_hidden(c3_7__trees_2,c1_7__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,dt_c3_7__trees_2,e3_7__trees_2,e1_7__trees_2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_finseq_1,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_numbers,dt_m2_finseq_1,cc1_nat_1,cc2_nat_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc2_trees_1,existence_m1_subset_1,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_subset_1,dt_m1_trees_1,dt_c2_7__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_c1_7__trees_2,dt_c3_7__trees_2,dt_c4_7__trees_2,de_c4_7__trees_2,t1_subset,t7_boole,e5_7__trees_2]),
    [interesting(0.8),file(trees_2,e6_7__trees_2),[file(trees_2,e6_7__trees_2)]]).

fof(i7_7__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i7_7__trees_2)]),
    [interesting(0.8),trivial,file(trees_2,i7_7__trees_2)]).

fof(i6_7__trees_2,plain,(
    r2_hidden(c3_7__trees_2,c1_7__trees_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,dt_c3_7__trees_2,e3_7__trees_2,e1_7__trees_2])],[e6_7__trees_2,i7_7__trees_2]),
    [interesting(0.8),file(trees_2,i6_7__trees_2),[file(trees_2,i6_7__trees_2)]]).

fof(i5_7__trees_2,plain,(
    ~ ( r2_hidden(c3_7__trees_2,c2_7__trees_2)
      & ~ r2_hidden(c3_7__trees_2,c1_7__trees_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,dt_c3_7__trees_2,e1_7__trees_2]),discharge_asm(discharge,[e3_7__trees_2])],[e3_7__trees_2,i6_7__trees_2]),
    [interesting(0.8),file(trees_2,i5_7__trees_2),[file(trees_2,i5_7__trees_2)]]).

fof(i5_7_tmp__trees_2,plain,(
    ~ ( r2_hidden(c3_7__trees_2,c2_7__trees_2)
      & ~ r2_hidden(c3_7__trees_2,c1_7__trees_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,e1_7__trees_2]),discharge_asm(discharge,[dt_c3_7__trees_2])],[dt_c3_7__trees_2,i5_7__trees_2]),
    [interesting(0.8),i4_7__trees_2]).

fof(i4_7__trees_2,plain,(
    r1_tarski(c2_7__trees_2,c1_7__trees_2) ),
    inference(let,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,e1_7__trees_2])],[i5_7_tmp__trees_2,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc2_trees_1,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_7__trees_2,dt_c2_7__trees_2,d3_tarski,dh_c3_7__trees_2]),
    [interesting(0.8),file(trees_2,i4_7__trees_2),[file(trees_2,i4_7__trees_2)]]).

fof(i3_7__trees_2,plain,(
    c1_7__trees_2 = c2_7__trees_2 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2,e1_7__trees_2])],[rc1_finset_1,rc1_relat_1,rc2_relat_1,rc2_trees_1,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,dt_c1_7__trees_2,dt_c2_7__trees_2,d10_xboole_0,e2_7__trees_2,i4_7__trees_2]),
    [interesting(0.8),file(trees_2,i3_7__trees_2),[file(trees_2,i3_7__trees_2)]]).

fof(i2_7__trees_2,plain,
    ( ! [A] : 
        ( m2_finseq_1(A,k5_numbers)
       => ( r2_hidden(A,c1_7__trees_2)
        <=> r2_hidden(A,c2_7__trees_2) ) )
   => c1_7__trees_2 = c2_7__trees_2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__trees_2,dt_c2_7__trees_2]),discharge_asm(discharge,[e1_7__trees_2])],[e1_7__trees_2,i3_7__trees_2]),
    [interesting(0.8),file(trees_2,i2_7__trees_2),[file(trees_2,i2_7__trees_2)]]).

fof(i2_7_tmp__trees_2,plain,
    ( ( ~ v1_xboole_0(c2_7__trees_2)
      & v1_trees_1(c2_7__trees_2) )
   => ( ! [A] : 
          ( m2_finseq_1(A,k5_numbers)
         => ( r2_hidden(A,c1_7__trees_2)
          <=> r2_hidden(A,c2_7__trees_2) ) )
     => c1_7__trees_2 = c2_7__trees_2 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__trees_2]),discharge_asm(discharge,[dt_c2_7__trees_2])],[dt_c2_7__trees_2,i2_7__trees_2]),
    [interesting(0.8),i1_7__trees_2]).

fof(i1_7__trees_2,plain,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ( r2_hidden(B,c1_7__trees_2)
            <=> r2_hidden(B,A) ) )
       => c1_7__trees_2 = A ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__trees_2])],[i2_7_tmp__trees_2,dh_c2_7__trees_2]),
    [interesting(0.8),file(trees_2,i1_7__trees_2),[file(trees_2,i1_7__trees_2)]]).

fof(i1_7_tmp__trees_2,plain,
    ( ( ~ v1_xboole_0(c1_7__trees_2)
      & v1_trees_1(c1_7__trees_2) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & v1_trees_1(A) )
       => ( ! [B] : 
              ( m2_finseq_1(B,k5_numbers)
             => ( r2_hidden(B,c1_7__trees_2)
              <=> r2_hidden(B,A) ) )
         => c1_7__trees_2 = A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__trees_2])],[dt_c1_7__trees_2,i1_7__trees_2]),
    [interesting(1),t7_trees_2]).

fof(t7_trees_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( ! [C] : 
                ( m2_finseq_1(C,k5_numbers)
               => ( r2_hidden(C,A)
                <=> r2_hidden(C,B) ) )
           => A = B ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__trees_2,dh_c1_7__trees_2]),
    [interesting(1),file(trees_2,t7_trees_2),[file(trees_2,t7_trees_2)]]).