% Mizar ND problem: t5_bintree1,bintree1,52,29 
fof(dh_c1_3__bintree1,definition,
    ( ( ( ~ v1_xboole_0(c1_3__bintree1)
        & v1_trees_1(c1_3__bintree1) )
     => ! [A] : 
          ( m1_trees_1(A,c1_3__bintree1)
         => ( k1_trees_2(c1_3__bintree1,A) = k1_xboole_0
          <=> r2_hidden(A,k3_trees_1(c1_3__bintree1)) ) ) )
   => ! [B] : 
        ( ( ~ v1_xboole_0(B)
          & v1_trees_1(B) )
       => ! [C] : 
            ( m1_trees_1(C,B)
           => ( k1_trees_2(B,C) = k1_xboole_0
            <=> r2_hidden(C,k3_trees_1(B)) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__bintree1),file(bintree1,c1_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,c1_3__bintree1)]).

fof(dh_c2_3__bintree1,definition,
    ( ( m1_trees_1(c2_3__bintree1,c1_3__bintree1)
     => ( k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0
      <=> r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ) )
   => ! [A] : 
        ( m1_trees_1(A,c1_3__bintree1)
       => ( k1_trees_2(c1_3__bintree1,A) = k1_xboole_0
        <=> r2_hidden(A,k3_trees_1(c1_3__bintree1)) ) ) ),
    introduced(definition,[new_symbol(c2_3__bintree1),file(bintree1,c2_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,c2_3__bintree1)]).

fof(e1_3_1__bintree1,assumption,(
    k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0 ),
    introduced(assumption,[file(bintree1,e1_3_1__bintree1)]),
    [interesting(0.65),axiom,file(bintree1,e1_3_1__bintree1)]).

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_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

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(cc7_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_trees_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_trees_3(A) ) ) ),
    file(trees_3,cc7_trees_3),
    [interesting(0.9),axiom,file(trees_3,cc7_trees_3)]).

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(fc8_trees_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v5_trees_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v5_trees_3(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B))
        & v4_trees_3(k7_finseq_1(A,B))
        & v5_trees_3(k7_finseq_1(A,B)) ) ) ),
    file(trees_3,fc8_trees_3),
    [interesting(0.9),axiom,file(trees_3,fc8_trees_3)]).

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

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(rc5_trees_3,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v4_trees_3(A)
      & v5_trees_3(A) ) ),
    file(trees_3,rc5_trees_3),
    [interesting(0.9),axiom,file(trees_3,rc5_trees_3)]).

fof(rc7_trees_3,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v4_trees_3(A)
      & v5_trees_3(A) ) ),
    file(trees_3,rc7_trees_3),
    [interesting(0.9),axiom,file(trees_3,rc7_trees_3)]).

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(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_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_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_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k13_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_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_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(fc13_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & ~ v1_xboole_0(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v4_trees_3(k5_finseq_1(A))
        & v5_trees_3(k5_finseq_1(A)) ) ) ),
    file(trees_3,fc13_trees_3),
    [interesting(0.9),axiom,file(trees_3,fc13_trees_3)]).

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(fc21_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( ~ v1_xboole_0(k3_trees_1(A))
        & v1_finset_1(k3_trees_1(A)) ) ) ),
    file(trees_3,fc21_trees_3),
    [interesting(0.9),axiom,file(trees_3,fc21_trees_3)]).

fof(fc7_trees_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v4_trees_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v4_trees_3(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B))
        & v4_trees_3(k7_finseq_1(A,B)) ) ) ),
    file(trees_3,fc7_trees_3),
    [interesting(0.9),axiom,file(trees_3,fc7_trees_3)]).

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(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

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(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(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(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_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_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(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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_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(redefinition_m2_finseq_2,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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_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_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k5_finseq_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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_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_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_dtconstr,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k3_finseq_2(A))
     => v1_finseq_1(B) ) ),
    file(dtconstr,cc1_dtconstr),
    [interesting(0.9),axiom,file(dtconstr,cc1_dtconstr)]).

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_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc10_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & ~ v1_xboole_0(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v4_trees_3(k5_finseq_1(A)) ) ) ),
    file(trees_3,fc10_trees_3),
    [interesting(0.9),axiom,file(trees_3,fc10_trees_3)]).

fof(fc12_finseq_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]).

fof(fc13_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(A,B))
        & v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,fc13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]).

fof(fc14_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & ~ v1_xboole_0(B)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k7_finseq_1(B,A))
        & v1_relat_1(k7_finseq_1(B,A))
        & v1_funct_1(k7_finseq_1(B,A))
        & v1_finset_1(k7_finseq_1(B,A))
        & v1_finseq_1(k7_finseq_1(B,A)) ) ) ),
    file(finseq_1,fc14_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc14_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(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(fc3_finseq_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]).

fof(fc4_finseq_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

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_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

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(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_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_k12_finseq_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k12_finseq_1(A,B) = k5_finseq_1(B) ) ),
    file(finseq_1,k12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]).

fof(redefinition_k3_lang1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k3_lang1(A,B) = k5_finseq_1(B) ) ),
    file(lang1,k3_lang1),
    [interesting(0.9),axiom,file(lang1,k3_lang1)]).

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

fof(redefinition_k8_finseq_1,definition,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ),
    file(finseq_1,k8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k8_finseq_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_k12_finseq_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_1(k12_finseq_1(A,B),A) ) ),
    file(finseq_1,k12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]).

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

fof(dt_k3_lang1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_2(k3_lang1(A,B),A,k3_finseq_2(A)) ) ),
    file(lang1,k3_lang1),
    [interesting(0.9),axiom,file(lang1,k3_lang1)]).

fof(dt_k3_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)) ) ),
    file(trees_1,k3_trees_1),
    [interesting(0.9),axiom,file(trees_1,k3_trees_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_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k7_finseq_1)]).

fof(dt_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ),
    file(finseq_1,k8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k8_finseq_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(dt_c1_3__bintree1,assumption,
    ( ~ v1_xboole_0(c1_3__bintree1)
    & v1_trees_1(c1_3__bintree1) ),
    introduced(assumption,[file(bintree1,c1_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,c1_3__bintree1)]).

fof(dt_c2_3__bintree1,assumption,(
    m1_trees_1(c2_3__bintree1,c1_3__bintree1) ),
    introduced(assumption,[file(bintree1,c2_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,c2_3__bintree1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_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(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(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(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_2_0_bintree1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_trees_1(B)
        & m1_trees_1(C,B) )
     => ( r2_hidden(A,a_2_0_bintree1(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k7_finseq_1(C,k3_lang1(k1_numbers,D))
            & r2_hidden(k7_finseq_1(C,k3_lang1(k1_numbers,D)),B) ) ) ) ),
    file(bintree1,a_2_0_bintree1),
    [interesting(0.9),axiom,file(bintree1,a_2_0_bintree1)]).

fof(fc4_trees_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & m1_subset_1(B,A) )
     => v1_finset_1(k1_trees_2(A,B)) ) ),
    file(trees_2,fc4_trees_2),
    [interesting(0.9),axiom,file(trees_2,fc4_trees_2)]).

fof(dt_k1_trees_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k1_trees_2(A,B),k1_zfmisc_1(A)) ) ),
    file(trees_2,k1_trees_2),
    [interesting(0.9),axiom,file(trees_2,k1_trees_2)]).

fof(fraenkel_a_2_1_trees_2,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_trees_1(B)
        & m1_trees_1(C,B) )
     => ( r2_hidden(A,a_2_1_trees_2(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D))
            & r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)),B) ) ) ) ),
    file(trees_2,a_2_1_trees_2),
    [interesting(0.9),axiom,file(trees_2,a_2_1_trees_2)]).

fof(d5_trees_2,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => k1_trees_2(A,B) = a_2_1_trees_2(A,B) ) ) ),
    file(trees_2,d5_trees_2),
    [interesting(0.9),axiom,file(trees_2,d5_trees_2)]).

fof(e2_3_1__bintree1,plain,(
    ~ r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,0)),a_2_0_bintree1(c1_3__bintree1,c2_3__bintree1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e1_3_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_fraenkel,cc1_relset_1,cc2_arytm_3,fc4_subset_1,rc1_arytm_3,rc1_fraenkel,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc3_arytm_3,cc7_trees_3,fc16_finseq_1,fc5_membered,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc4_finseq_1,rc5_trees_3,rc7_trees_3,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_k8_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k3_lang1,redefinition_m1_trees_1,dt_k1_numbers,dt_k1_trees_2,dt_k1_xboole_0,dt_k3_lang1,dt_k7_finseq_1,dt_m1_trees_1,dt_c1_3__bintree1,dt_c2_3__bintree1,cc15_membered,fc2_finseq_1,fc2_membered,fc6_membered,spc0_boole,t1_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_2_0_bintree1,fraenkel_a_2_1_trees_2,spc0_numerals,spc0_boole,e1_3_1__bintree1,d5_trees_2]),
    [interesting(0.65),file(bintree1,e2_3_1__bintree1),[file(bintree1,e2_3_1__bintree1)]]).

fof(e3_3_1__bintree1,plain,(
    ~ r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,0)),c1_3__bintree1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e1_3_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_arytm_3,cc1_fraenkel,cc2_arytm_3,cc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc6_membered,cc9_membered,fc13_trees_3,fc16_finseq_1,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,fc7_trees_3,fc9_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_dtconstr,cc1_finseq_1,cc4_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_finseq_1,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k3_lang1,dt_k1_numbers,dt_k3_lang1,dt_k7_finseq_1,dt_c1_3__bintree1,dt_c2_3__bintree1,fc2_membered,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_0_bintree1,spc0_numerals,spc0_boole,e2_3_1__bintree1]),
    [interesting(0.65),file(bintree1,e3_3_1__bintree1),[file(bintree1,e3_3_1__bintree1)]]).

fof(t53_modal_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ( r2_hidden(B,k3_trees_1(A))
          <=> ~ r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0)),A) ) ) ) ),
    file(modal_1,t53_modal_1),
    [interesting(0.9),axiom,file(modal_1,t53_modal_1)]).

fof(e4_3_1__bintree1,plain,(
    r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e1_3_1__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,cc7_trees_3,fc4_subset_1,fc8_trees_3,rc1_fraenkel,rc2_finseq_1,rc5_trees_3,rc7_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,fc13_trees_3,fc16_finseq_1,fc21_trees_3,fc7_trees_3,fc9_finseq_1,rc1_arytm_3,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_subset_1,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k12_finseq_1,dt_k1_numbers,dt_k3_lang1,dt_k3_trees_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_3__bintree1,dt_c2_3__bintree1,cc15_membered,fc2_membered,spc0_boole,t1_subset,t6_boole,t7_boole,spc0_numerals,spc0_boole,e3_3_1__bintree1,t53_modal_1]),
    [interesting(0.65),file(bintree1,e4_3_1__bintree1),[file(bintree1,e4_3_1__bintree1)]]).

fof(i2_3_1__bintree1,theorem,(
    $true ),
    introduced(tautology,[file(bintree1,i2_3_1__bintree1)]),
    [interesting(0.65),trivial,file(bintree1,i2_3_1__bintree1)]).

fof(i1_3_1__bintree1,plain,(
    r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e1_3_1__bintree1])],[e4_3_1__bintree1,i2_3_1__bintree1]),
    [interesting(0.65),file(bintree1,i1_3_1__bintree1),[file(bintree1,i1_3_1__bintree1)]]).

fof(e1_3__bintree1,plain,
    ( k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0
   => r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1]),discharge_asm(discharge,[e1_3_1__bintree1])],[e1_3_1__bintree1,i1_3_1__bintree1]),
    [interesting(0.8),file(bintree1,e1_3__bintree1),[file(bintree1,e1_3__bintree1)]]).

fof(e2_3__bintree1,assumption,(
    r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ),
    introduced(assumption,[file(bintree1,e2_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,e2_3__bintree1)]).

fof(e4_3__bintree1,assumption,(
    k1_trees_2(c1_3__bintree1,c2_3__bintree1) != k1_xboole_0 ),
    introduced(assumption,[file(bintree1,e4_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,e4_3__bintree1)]).

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(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(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(dt_k1_trees_1,axiom,(
    $true ),
    file(trees_1,k1_trees_1),
    [interesting(0.9),axiom,file(trees_1,k1_trees_1)]).

fof(dh_c3_3__bintree1,definition,
    ( ? [A] : m1_subset_1(A,k1_trees_2(c1_3__bintree1,c2_3__bintree1))
   => m1_subset_1(c3_3__bintree1,k1_trees_2(c1_3__bintree1,c2_3__bintree1)) ),
    introduced(definition,[new_symbol(c3_3__bintree1),file(bintree1,c3_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,c3_3__bintree1)]).

fof(e5_3__bintree1,plain,(
    ? [A] : m1_subset_1(A,k1_trees_2(c1_3__bintree1,c2_3__bintree1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,fc4_subset_1,rc1_arytm_3,rc2_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_finseq_1,cc3_arytm_3,cc6_membered,fc2_membered,fc4_trees_2,fc5_membered,rc1_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_numbers,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc9_membered,fc2_finseq_1,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_trees_1,redefinition_m1_trees_1,dt_k1_zfmisc_1,dt_m1_trees_1,cc15_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_trees_2,dt_m1_subset_1,dt_c1_3__bintree1,dt_c2_3__bintree1]),
    [interesting(0.8),file(bintree1,e5_3__bintree1),[file(bintree1,e5_3__bintree1)]]).

fof(dt_c3_3__bintree1,plain,(
    m1_subset_1(c3_3__bintree1,k1_trees_2(c1_3__bintree1,c2_3__bintree1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1])],[dh_c3_3__bintree1,e5_3__bintree1]),
    [interesting(0.8),file(bintree1,c3_3__bintree1),[file(bintree1,c3_3__bintree1)]]).

fof(dh_c4_3__bintree1,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & c3_3__bintree1 = k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,A))
        & r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,A)),c1_3__bintree1) )
   => ( m2_subset_1(c4_3__bintree1,k1_numbers,k5_numbers)
      & c3_3__bintree1 = k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,c4_3__bintree1))
      & r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,c4_3__bintree1)),c1_3__bintree1) ) ),
    introduced(definition,[new_symbol(c4_3__bintree1),file(bintree1,c4_3__bintree1)]),
    [interesting(0.8),axiom,file(bintree1,c4_3__bintree1)]).

fof(e6_3__bintree1,plain,(
    r2_hidden(c3_3__bintree1,k1_trees_2(c1_3__bintree1,c2_3__bintree1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,fc4_subset_1,rc1_arytm_3,rc2_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc3_arytm_3,cc6_membered,fc2_membered,fc5_membered,rc4_finseq_1,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m2_finseq_1,cc9_membered,existence_m1_subset_1,existence_m1_trees_1,redefinition_m1_trees_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m1_trees_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc4_trees_2,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_trees_2,dt_k1_xboole_0,dt_c1_3__bintree1,dt_c2_3__bintree1,dt_c3_3__bintree1,fc2_finseq_1,fc6_membered,t1_subset,t6_boole,t7_boole,e4_3__bintree1]),
    [interesting(0.8),file(bintree1,e6_3__bintree1),[file(bintree1,e6_3__bintree1)]]).

fof(e7_3__bintree1,plain,(
    r2_hidden(c3_3__bintree1,a_2_0_bintree1(c1_3__bintree1,c2_3__bintree1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[cc1_fraenkel,rc1_fraenkel,existence_m1_finseq_2,existence_m1_relset_1,dt_k13_finseq_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,cc7_trees_3,fc16_finseq_1,fc4_subset_1,fc7_trees_3,fc8_trees_3,fc9_finseq_1,rc1_arytm_3,rc2_finseq_1,rc5_trees_3,rc7_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_dtconstr,cc1_finseq_1,cc3_arytm_3,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,fc5_membered,rc1_finseq_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc2_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_m1_trees_1,dt_k1_trees_2,dt_m1_trees_1,dt_c1_3__bintree1,dt_c2_3__bintree1,dt_c3_3__bintree1,cc15_membered,t1_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_2_0_bintree1,fraenkel_a_2_1_trees_2,e6_3__bintree1,d5_trees_2]),
    [interesting(0.8),file(bintree1,e7_3__bintree1),[file(bintree1,e7_3__bintree1)]]).

fof(e8_3__bintree1,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & c3_3__bintree1 = k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,A))
      & r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,A)),c1_3__bintree1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_fraenkel,cc7_trees_3,fc8_trees_3,rc1_fraenkel,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc13_trees_3,fc16_finseq_1,fc2_finseq_1,fc4_trees_2,fc6_membered,fc7_trees_3,fc9_finseq_1,rc1_arytm_3,rc1_membered,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_2,dt_k1_trees_2,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_dtconstr,cc1_finseq_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,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_subset_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_m2_subset_1,dt_c1_3__bintree1,dt_c2_3__bintree1,dt_c3_3__bintree1,fc2_membered,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_0_bintree1,e7_3__bintree1]),
    [interesting(0.8),file(bintree1,e8_3__bintree1),[file(bintree1,e8_3__bintree1)]]).

fof(dt_c4_3__bintree1,plain,(
    m2_subset_1(c4_3__bintree1,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[dh_c4_3__bintree1,e8_3__bintree1]),
    [interesting(0.8),file(bintree1,c4_3__bintree1),[file(bintree1,c4_3__bintree1)]]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(t18_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r1_xreal_0(0,A) ) ),
    file(nat_1,t18_nat_1),
    [interesting(0.9),axiom,file(nat_1,t18_nat_1)]).

fof(e10_3__bintree1,plain,(
    r1_xreal_0(0,c4_3__bintree1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_finseq_1,cc2_arytm_3,rc1_arytm_3,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t3_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc2_membered,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c4_3__bintree1,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,t18_nat_1]),
    [interesting(0.8),file(bintree1,e10_3__bintree1),[file(bintree1,e10_3__bintree1)]]).

fof(e3_3__bintree1,plain,(
    ~ r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,0)),c1_3__bintree1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e2_3__bintree1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,cc1_relset_1,cc7_trees_3,fc4_subset_1,fc8_trees_3,rc1_fraenkel,rc2_finseq_1,rc5_trees_3,rc7_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_arytm_3,cc2_arytm_3,fc13_trees_3,fc16_finseq_1,fc21_trees_3,fc7_trees_3,fc9_finseq_1,rc1_arytm_3,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_subset_1,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_membered,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k12_finseq_1,dt_k1_numbers,dt_k3_lang1,dt_k3_trees_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_3__bintree1,dt_c2_3__bintree1,cc15_membered,fc2_membered,spc0_boole,t1_subset,t6_boole,t7_boole,spc0_numerals,spc0_boole,e2_3__bintree1,t53_modal_1]),
    [interesting(0.8),file(bintree1,e3_3__bintree1),[file(bintree1,e3_3__bintree1)]]).

fof(e9_3__bintree1,plain,
    ( c3_3__bintree1 = k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,c4_3__bintree1))
    & r2_hidden(k7_finseq_1(c2_3__bintree1,k3_lang1(k1_numbers,c4_3__bintree1)),c1_3__bintree1) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[dh_c4_3__bintree1,e8_3__bintree1]),
    [interesting(0.8),file(bintree1,e9_3__bintree1),[file(bintree1,e9_3__bintree1)]]).

fof(d5_trees_1,definition,(
    ! [A] : 
      ( v1_trees_1(A)
    <=> ( r1_tarski(A,k13_finseq_1(k5_numbers))
        & ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ( r2_hidden(B,A)
             => r1_tarski(k1_trees_1(B),A) ) )
        & ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A)
                        & r1_xreal_0(D,C) )
                     => r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,D)),A) ) ) ) ) ) ) ),
    file(trees_1,d5_trees_1),
    [interesting(0.9),axiom,file(trees_1,d5_trees_1)]).

fof(e11_3__bintree1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e2_3__bintree1,dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[cc7_trees_3,fc8_trees_3,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc13_trees_3,fc2_finseq_1,fc4_subset_1,fc4_trees_2,fc6_membered,fc7_trees_3,rc1_arytm_3,rc1_membered,rc2_finseq_1,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_trees_2,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_dtconstr,cc1_finseq_1,cc1_fraenkel,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,rc1_finseq_1,rc1_fraenkel,rc1_subset_1,rc2_subset_1,t1_numerals,t1_real,t2_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k13_finseq_1,dt_k1_numbers,dt_k1_trees_1,dt_k3_lang1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_3__bintree1,dt_c2_3__bintree1,dt_c3_3__bintree1,dt_c4_3__bintree1,fc16_finseq_1,fc2_membered,fc9_finseq_1,t1_subset,t3_subset,t7_boole,spc0_numerals,spc0_boole,e10_3__bintree1,e3_3__bintree1,e9_3__bintree1,d5_trees_1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.8),file(bintree1,e11_3__bintree1),[file(bintree1,e11_3__bintree1)]]).

fof(i6_3__bintree1,theorem,(
    $true ),
    introduced(tautology,[file(bintree1,i6_3__bintree1)]),
    [interesting(0.8),trivial,file(bintree1,i6_3__bintree1)]).

fof(i5_3__bintree1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e2_3__bintree1,dt_c1_3__bintree1,dt_c2_3__bintree1,e4_3__bintree1])],[e11_3__bintree1,i6_3__bintree1]),
    [interesting(0.8),file(bintree1,i5_3__bintree1),[file(bintree1,i5_3__bintree1)]]).

fof(i4_3__bintree1,plain,(
    k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0 ),
    inference(discharge_asm,[status(thm),assumptions([e2_3__bintree1,dt_c1_3__bintree1,dt_c2_3__bintree1]),discharge_asm(discharge,[e4_3__bintree1])],[e4_3__bintree1,i5_3__bintree1]),
    [interesting(0.8),file(bintree1,i4_3__bintree1),[file(bintree1,i4_3__bintree1)]]).

fof(i3_3__bintree1,plain,
    ( r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1))
   => k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1]),discharge_asm(discharge,[e2_3__bintree1])],[e2_3__bintree1,i4_3__bintree1]),
    [interesting(0.8),file(bintree1,i3_3__bintree1),[file(bintree1,i3_3__bintree1)]]).

fof(i2_3__bintree1,plain,
    ( k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0
  <=> r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__bintree1,dt_c2_3__bintree1])],[e1_3__bintree1,i3_3__bintree1]),
    [interesting(0.8),file(bintree1,i2_3__bintree1),[file(bintree1,i2_3__bintree1)]]).

fof(i2_3_tmp__bintree1,plain,
    ( m1_trees_1(c2_3__bintree1,c1_3__bintree1)
   => ( k1_trees_2(c1_3__bintree1,c2_3__bintree1) = k1_xboole_0
    <=> r2_hidden(c2_3__bintree1,k3_trees_1(c1_3__bintree1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bintree1]),discharge_asm(discharge,[dt_c2_3__bintree1])],[dt_c2_3__bintree1,i2_3__bintree1]),
    [interesting(0.8),i1_3__bintree1]).

fof(i1_3__bintree1,plain,(
    ! [A] : 
      ( m1_trees_1(A,c1_3__bintree1)
     => ( k1_trees_2(c1_3__bintree1,A) = k1_xboole_0
      <=> r2_hidden(A,k3_trees_1(c1_3__bintree1)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bintree1])],[i2_3_tmp__bintree1,dh_c2_3__bintree1]),
    [interesting(0.8),file(bintree1,i1_3__bintree1),[file(bintree1,i1_3__bintree1)]]).

fof(i1_3_tmp__bintree1,plain,
    ( ( ~ v1_xboole_0(c1_3__bintree1)
      & v1_trees_1(c1_3__bintree1) )
   => ! [A] : 
        ( m1_trees_1(A,c1_3__bintree1)
       => ( k1_trees_2(c1_3__bintree1,A) = k1_xboole_0
        <=> r2_hidden(A,k3_trees_1(c1_3__bintree1)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__bintree1])],[dt_c1_3__bintree1,i1_3__bintree1]),
    [interesting(1),t5_bintree1]).

fof(t5_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ( k1_trees_2(A,B) = k1_xboole_0
          <=> r2_hidden(B,k3_trees_1(A)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__bintree1,dh_c1_3__bintree1]),
    [interesting(1),file(bintree1,t5_bintree1),[file(bintree1,t5_bintree1)]]).