% Mizar ND problem: t1_bintree2,bintree2,38,33 
fof(dh_c1_1__bintree2,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(A,k3_finseq_2(c1_1__bintree2))
             => r2_hidden(k7_relat_1(A,k2_finseq_1(B)),k3_finseq_2(c1_1__bintree2)) ) ) )
   => ! [C,D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D)
          & v1_finseq_1(D) )
       => ! [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
           => ( r2_hidden(D,k3_finseq_2(C))
             => r2_hidden(k7_relat_1(D,k2_finseq_1(E)),k3_finseq_2(C)) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__bintree2),file(bintree2,c1_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c1_1__bintree2)]).

fof(dh_c2_1__bintree2,definition,
    ( ( ( v1_relat_1(c2_1__bintree2)
        & v1_funct_1(c2_1__bintree2)
        & v1_finseq_1(c2_1__bintree2) )
     => ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
           => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(A)),k3_finseq_2(c1_1__bintree2)) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B) )
       => ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k3_finseq_2(c1_1__bintree2))
             => r2_hidden(k7_relat_1(B,k2_finseq_1(C)),k3_finseq_2(c1_1__bintree2)) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__bintree2),file(bintree2,c2_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c2_1__bintree2)]).

fof(dh_c3_1__bintree2,definition,
    ( ( m2_subset_1(c3_1__bintree2,k1_numbers,k5_numbers)
     => ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
       => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(c3_1__bintree2)),k3_finseq_2(c1_1__bintree2)) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
         => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(A)),k3_finseq_2(c1_1__bintree2)) ) ) ),
    introduced(definition,[new_symbol(c3_1__bintree2),file(bintree2,c3_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c3_1__bintree2)]).

fof(e1_1__bintree2,assumption,(
    r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2)) ),
    introduced(assumption,[file(bintree2,e1_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,e1_1__bintree2)]).

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(rc1_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

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_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_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_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_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_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(rc5_trees_9,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_xboole_0(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(trees_9,rc5_trees_9),
    [interesting(0.9),axiom,file(trees_9,rc5_trees_9)]).

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

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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

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(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(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(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(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

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(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_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(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_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_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_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(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(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(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(rc9_trees_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & ~ v1_xboole_0(C) ) ) ),
    file(trees_2,rc9_trees_2),
    [interesting(0.9),axiom,file(trees_2,rc9_trees_2)]).

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_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

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_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(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_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(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_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_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_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

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_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(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_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_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(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_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(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(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(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_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_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(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(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(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(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_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_2,definition,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]).

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_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k13_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_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]).

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(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(dt_c1_1__bintree2,assumption,(
    $true ),
    introduced(assumption,[file(bintree2,c1_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c1_1__bintree2)]).

fof(dt_c2_1__bintree2,assumption,
    ( v1_relat_1(c2_1__bintree2)
    & v1_funct_1(c2_1__bintree2)
    & v1_finseq_1(c2_1__bintree2) ),
    introduced(assumption,[file(bintree2,c2_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c2_1__bintree2)]).

fof(dt_c3_1__bintree2,assumption,(
    m2_subset_1(c3_1__bintree2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(bintree2,c3_1__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c3_1__bintree2)]).

fof(fc16_finseq_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k13_finseq_1(A))
      & v1_fraenkel(k13_finseq_1(A)) ) ),
    file(finseq_1,fc16_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc16_finseq_1)]).

fof(fc9_finseq_1,theorem,(
    ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ),
    file(finseq_1,fc9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc9_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(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(d11_finseq_1,definition,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,d11_finseq_1)]).

fof(e2_1__bintree2,plain,(
    m2_finseq_1(c2_1__bintree2,c1_1__bintree2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bintree2,dt_c2_1__bintree2,e1_1__bintree2])],[reflexivity_r1_tarski,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_margrel1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,existence_m1_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_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,fc14_finset_1,fc1_margrel1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc4_subset_1,rc1_finset_1,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_subset_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k5_numbers,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,rc1_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k3_finseq_2,dt_m2_finseq_1,dt_c1_1__bintree2,dt_c2_1__bintree2,fc16_finseq_1,fc9_finseq_1,t1_subset,t7_boole,e1_1__bintree2,d11_finseq_1]),
    [interesting(0.8),file(bintree2,e2_1__bintree2),[file(bintree2,e2_1__bintree2)]]).

fof(t23_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B) ) ) ),
    file(finseq_1,t23_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t23_finseq_1)]).

fof(e3_1__bintree2,plain,(
    m2_finseq_1(k7_relat_1(c2_1__bintree2,k2_finseq_1(c3_1__bintree2)),c1_1__bintree2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bintree2,dt_c1_1__bintree2,dt_c2_1__bintree2,e1_1__bintree2])],[rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc2_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc1_finset_1,cc1_relset_1,cc2_finset_1,cc3_xreal_0,cc4_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc14_finset_1,fc1_ordinal2,fc4_subset_1,rc1_finset_1,rc1_nat_1,rc1_subset_1,rc2_finseq_1,rc2_nat_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc1_finseq_1,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc5_xreal_0,fc1_finseq_1,fc1_subset_1,rc1_finseq_1,rc1_xreal_0,t3_subset,existence_m2_finseq_1,redefinition_k2_finseq_1,redefinition_m2_finseq_1,dt_k2_finseq_1,dt_k7_relat_1,dt_m2_finseq_1,dt_c1_1__bintree2,dt_c2_1__bintree2,dt_c3_1__bintree2,cc1_xreal_0,cc3_nat_1,e2_1__bintree2,t23_finseq_1]),
    [interesting(0.8),file(bintree2,e3_1__bintree2),[file(bintree2,e3_1__bintree2)]]).

fof(e4_1__bintree2,plain,(
    r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(c3_1__bintree2)),k3_finseq_2(c1_1__bintree2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_1__bintree2,dt_c1_1__bintree2,dt_c2_1__bintree2,e1_1__bintree2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_margrel1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc1_relset_1,cc2_finset_1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc1_margrel1,fc1_ordinal2,fc2_finseq_1,fc4_subset_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_nat_1,cc3_nat_1,fc1_finseq_1,fc1_subset_1,rc1_finseq_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k2_finseq_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k2_finseq_1,dt_k3_finseq_2,dt_k7_relat_1,dt_m2_finseq_1,dt_c1_1__bintree2,dt_c2_1__bintree2,dt_c3_1__bintree2,fc16_finseq_1,fc9_finseq_1,t1_subset,t7_boole,e3_1__bintree2,d11_finseq_1]),
    [interesting(0.8),file(bintree2,e4_1__bintree2),[file(bintree2,e4_1__bintree2)]]).

fof(i5_1__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i5_1__bintree2)]),
    [interesting(0.8),trivial,file(bintree2,i5_1__bintree2)]).

fof(i4_1__bintree2,plain,(
    r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(c3_1__bintree2)),k3_finseq_2(c1_1__bintree2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_1__bintree2,dt_c1_1__bintree2,dt_c2_1__bintree2,e1_1__bintree2])],[e4_1__bintree2,i5_1__bintree2]),
    [interesting(0.8),file(bintree2,i4_1__bintree2),[file(bintree2,i4_1__bintree2)]]).

fof(i3_1__bintree2,plain,
    ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
   => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(c3_1__bintree2)),k3_finseq_2(c1_1__bintree2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_1__bintree2,dt_c1_1__bintree2,dt_c2_1__bintree2]),discharge_asm(discharge,[e1_1__bintree2])],[e1_1__bintree2,i4_1__bintree2]),
    [interesting(0.8),file(bintree2,i3_1__bintree2),[file(bintree2,i3_1__bintree2)]]).

fof(i3_1_tmp__bintree2,plain,
    ( m2_subset_1(c3_1__bintree2,k1_numbers,k5_numbers)
   => ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
     => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(c3_1__bintree2)),k3_finseq_2(c1_1__bintree2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bintree2,dt_c2_1__bintree2]),discharge_asm(discharge,[dt_c3_1__bintree2])],[dt_c3_1__bintree2,i3_1__bintree2]),
    [interesting(0.8),i2_1__bintree2]).

fof(i2_1__bintree2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
       => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(A)),k3_finseq_2(c1_1__bintree2)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__bintree2,dt_c2_1__bintree2])],[i3_1_tmp__bintree2,dh_c3_1__bintree2]),
    [interesting(0.8),file(bintree2,i2_1__bintree2),[file(bintree2,i2_1__bintree2)]]).

fof(i2_1_tmp__bintree2,plain,
    ( ( v1_relat_1(c2_1__bintree2)
      & v1_funct_1(c2_1__bintree2)
      & v1_finseq_1(c2_1__bintree2) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r2_hidden(c2_1__bintree2,k3_finseq_2(c1_1__bintree2))
         => r2_hidden(k7_relat_1(c2_1__bintree2,k2_finseq_1(A)),k3_finseq_2(c1_1__bintree2)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bintree2]),discharge_asm(discharge,[dt_c2_1__bintree2])],[dt_c2_1__bintree2,i2_1__bintree2]),
    [interesting(0.8),i1_1__bintree2]).

fof(i1_1__bintree2,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k3_finseq_2(c1_1__bintree2))
           => r2_hidden(k7_relat_1(A,k2_finseq_1(B)),k3_finseq_2(c1_1__bintree2)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__bintree2])],[i2_1_tmp__bintree2,dh_c2_1__bintree2]),
    [interesting(0.8),file(bintree2,i1_1__bintree2),[file(bintree2,i1_1__bintree2)]]).

fof(i1_1_tmp__bintree2,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k3_finseq_2(c1_1__bintree2))
           => r2_hidden(k7_relat_1(A,k2_finseq_1(B)),k3_finseq_2(c1_1__bintree2)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__bintree2])],[dt_c1_1__bintree2,i1_1__bintree2]),
    [interesting(1),t1_bintree2]).

fof(t1_bintree2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k3_finseq_2(A))
           => r2_hidden(k7_relat_1(B,k2_finseq_1(C)),k3_finseq_2(A)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__bintree2,dh_c1_1__bintree2]),
    [interesting(1),file(bintree2,t1_bintree2),[file(bintree2,t1_bintree2)]]).