% Mizar ND problem: t8_trees_2,trees_2,169,47 
fof(dh_c1_9__trees_2,definition,
    ( ( ( ~ v1_xboole_0(c1_9__trees_2)
        & v1_trees_1(c1_9__trees_2) )
     => ! [A] : 
          ( m2_finseq_1(A,k5_numbers)
         => ( r2_hidden(A,c1_9__trees_2)
           => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,A,k4_trees_1(c1_9__trees_2,A)) ) ) )
   => ! [B] : 
        ( ( ~ v1_xboole_0(B)
          & v1_trees_1(B) )
       => ! [C] : 
            ( m2_finseq_1(C,k5_numbers)
           => ( r2_hidden(C,B)
             => B = k5_trees_1(B,C,k4_trees_1(B,C)) ) ) ) ),
    introduced(definition,[new_symbol(c1_9__trees_2),file(trees_2,c1_9__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c1_9__trees_2)]).

fof(dh_c2_9__trees_2,definition,
    ( ( m2_finseq_1(c2_9__trees_2,k5_numbers)
     => ( r2_hidden(c2_9__trees_2,c1_9__trees_2)
       => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)) ) )
   => ! [A] : 
        ( m2_finseq_1(A,k5_numbers)
       => ( r2_hidden(A,c1_9__trees_2)
         => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,A,k4_trees_1(c1_9__trees_2,A)) ) ) ),
    introduced(definition,[new_symbol(c2_9__trees_2),file(trees_2,c2_9__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c2_9__trees_2)]).

fof(e1_9__trees_2,assumption,(
    r2_hidden(c2_9__trees_2,c1_9__trees_2) ),
    introduced(assumption,[file(trees_2,e1_9__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,e1_9__trees_2)]).

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(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(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_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(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_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(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(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_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(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_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(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(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_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_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_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_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_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_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_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_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(fc1_trees_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & m1_subset_1(B,A) )
     => ( ~ v1_xboole_0(k4_trees_1(A,B))
        & v1_finset_1(k4_trees_1(A,B))
        & v1_trees_1(k4_trees_1(A,B)) ) ) ),
    file(trees_1,fc1_trees_1),
    [interesting(0.9),axiom,file(trees_1,fc1_trees_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(fc2_trees_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & m1_subset_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_finset_1(C)
        & v1_trees_1(C) )
     => ( ~ v1_xboole_0(k5_trees_1(A,B,C))
        & v1_finset_1(k5_trees_1(A,B,C))
        & v1_trees_1(k5_trees_1(A,B,C)) ) ) ),
    file(trees_1,fc2_trees_1),
    [interesting(0.9),axiom,file(trees_1,fc2_trees_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(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_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(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_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(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(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(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(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(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_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_k4_trees_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & m1_finseq_1(B,k5_numbers) )
     => ( ~ v1_xboole_0(k4_trees_1(A,B))
        & v1_trees_1(k4_trees_1(A,B)) ) ) ),
    file(trees_1,k4_trees_1),
    [interesting(0.9),axiom,file(trees_1,k4_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_k5_trees_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & m1_finseq_1(B,k5_numbers)
        & ~ v1_xboole_0(C)
        & v1_trees_1(C) )
     => ( ~ v1_xboole_0(k5_trees_1(A,B,C))
        & v1_trees_1(k5_trees_1(A,B,C)) ) ) ),
    file(trees_1,k5_trees_1),
    [interesting(0.9),axiom,file(trees_1,k5_trees_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_9__trees_2,assumption,
    ( ~ v1_xboole_0(c1_9__trees_2)
    & v1_trees_1(c1_9__trees_2) ),
    introduced(assumption,[file(trees_2,c1_9__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c1_9__trees_2)]).

fof(dt_c2_9__trees_2,assumption,(
    m2_finseq_1(c2_9__trees_2,k5_numbers) ),
    introduced(assumption,[file(trees_2,c2_9__trees_2)]),
    [interesting(0.8),axiom,file(trees_2,c2_9__trees_2)]).

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(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(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(dh_c1_9_1__trees_2,definition,
    ( ( m2_finseq_1(c1_9_1__trees_2,k5_numbers)
     => ( ( r2_hidden(c1_9_1__trees_2,c1_9__trees_2)
         => r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) )
        & ~ ( r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
            & ~ r2_hidden(c1_9_1__trees_2,c1_9__trees_2) ) ) )
   => ! [A] : 
        ( m2_finseq_1(A,k5_numbers)
       => ( ( r2_hidden(A,c1_9__trees_2)
           => r2_hidden(A,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) )
          & ~ ( r2_hidden(A,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
              & ~ r2_hidden(A,c1_9__trees_2) ) ) ) ),
    introduced(definition,[new_symbol(c1_9_1__trees_2),file(trees_2,c1_9_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_9_1__trees_2)]).

fof(e1_9_1_1__trees_2,assumption,(
    r2_hidden(c1_9_1__trees_2,c1_9__trees_2) ),
    introduced(assumption,[file(trees_2,e1_9_1_1__trees_2)]),
    [interesting(0.5),axiom,file(trees_2,e1_9_1_1__trees_2)]).

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(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(irreflexivity_r2_xboole_0,theorem,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r2_xboole_0)]).

fof(antisymmetry_r2_xboole_0,theorem,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r2_xboole_0)]).

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(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_c1_9_1__trees_2,assumption,(
    m2_finseq_1(c1_9_1__trees_2,k5_numbers) ),
    introduced(assumption,[file(trees_2,c1_9_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,c1_9_1__trees_2)]).

fof(e1_9_1_1_1__trees_2,assumption,(
    r2_xboole_0(c2_9__trees_2,c1_9_1__trees_2) ),
    introduced(assumption,[file(trees_2,e1_9_1_1_1__trees_2)]),
    [interesting(0.35),axiom,file(trees_2,e1_9_1_1_1__trees_2)]).

fof(dh_c1_9_1_1_1__trees_2,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & c1_9_1__trees_2 = k7_finseq_1(c2_9__trees_2,A) )
   => ( v1_relat_1(c1_9_1_1_1__trees_2)
      & v1_funct_1(c1_9_1_1_1__trees_2)
      & v1_finseq_1(c1_9_1_1_1__trees_2)
      & c1_9_1__trees_2 = k7_finseq_1(c2_9__trees_2,c1_9_1_1_1__trees_2) ) ),
    introduced(definition,[new_symbol(c1_9_1_1_1__trees_2),file(trees_2,c1_9_1_1_1__trees_2)]),
    [interesting(0.35),axiom,file(trees_2,c1_9_1_1_1__trees_2)]).

fof(d8_xboole_0,definition,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d8_xboole_0)]).

fof(e2_9_1_1_1__trees_2,plain,(
    r1_tarski(c2_9__trees_2,c1_9_1__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc2_finset_1,cc3_xreal_0,cc6_xreal_0,cc8_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_relat_1,rc2_finseq_1,rc2_relat_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_subset,t4_subset,t5_subset,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_finset_1,cc1_relat_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_numbers,fc1_ordinal2,rc1_nat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_nat_1,rc2_subset_1,rc2_xboole_0,rc3_nat_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_nat_1,cc2_nat_1,fc1_subset_1,reflexivity_r1_tarski,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,dt_c1_9_1__trees_2,dt_c2_9__trees_2,t3_subset,e1_9_1_1_1__trees_2,d8_xboole_0]),
    [interesting(0.35),file(trees_2,e2_9_1_1_1__trees_2),[file(trees_2,e2_9_1_1_1__trees_2)]]).

fof(t8_trees_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & B = k7_finseq_1(A,C) ) ) ) ) ),
    file(trees_1,t8_trees_1),
    [interesting(0.9),axiom,file(trees_1,t8_trees_1)]).

fof(e3_9_1_1_1__trees_2,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A)
      & c1_9_1__trees_2 = k7_finseq_1(c2_9__trees_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,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_finset_1,cc1_relat_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_numbers,fc1_ordinal2,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_subset_1,reflexivity_r1_tarski,dt_k7_finseq_1,dt_c1_9_1__trees_2,dt_c2_9__trees_2,cc1_finseq_1,rc1_finseq_1,t3_subset,e2_9_1_1_1__trees_2,t8_trees_1]),
    [interesting(0.35),file(trees_2,e3_9_1_1_1__trees_2),[file(trees_2,e3_9_1_1_1__trees_2)]]).

fof(dt_c1_9_1_1_1__trees_2,plain,
    ( v1_relat_1(c1_9_1_1_1__trees_2)
    & v1_funct_1(c1_9_1_1_1__trees_2)
    & v1_finseq_1(c1_9_1_1_1__trees_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[dh_c1_9_1_1_1__trees_2,e3_9_1_1_1__trees_2]),
    [interesting(0.35),file(trees_2,c1_9_1_1_1__trees_2),[file(trees_2,c1_9_1_1_1__trees_2)]]).

fof(de_c2_9_1_1_1__trees_2,definition,(
    c2_9_1_1_1__trees_2 = c1_9_1_1_1__trees_2 ),
    introduced(definition,[new_symbol(c2_9_1_1_1__trees_2),file(trees_2,c2_9_1_1_1__trees_2)]),
    [interesting(0.35),axiom,file(trees_2,c2_9_1_1_1__trees_2)]).

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(redefinition_k5_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(e4_9_1_1_1__trees_2,plain,(
    c1_9_1__trees_2 = k7_finseq_1(c2_9__trees_2,c1_9_1_1_1__trees_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[dh_c1_9_1_1_1__trees_2,e3_9_1_1_1__trees_2]),
    [interesting(0.35),file(trees_2,e4_9_1_1_1__trees_2),[file(trees_2,e4_9_1_1_1__trees_2)]]).

fof(t43_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))) ) ) ),
    file(finseq_1,t43_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t43_finseq_1)]).

fof(e5_9_1_1_1__trees_2,plain,
    ( r1_tarski(k2_relat_1(c1_9_1_1_1__trees_2),k5_relset_1(k5_numbers,k5_numbers,c1_9_1__trees_2))
    & r1_tarski(k5_relset_1(k5_numbers,k5_numbers,c1_9_1__trees_2),k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_finset_1,cc1_relat_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc13_finseq_1,fc14_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc2_finseq_1,reflexivity_r1_tarski,redefinition_k5_numbers,redefinition_k5_relset_1,dt_k2_relat_1,dt_k5_numbers,dt_k5_relset_1,dt_k7_finseq_1,dt_c1_9_1__trees_2,dt_c1_9_1_1_1__trees_2,dt_c2_9__trees_2,cc1_finseq_1,rc1_finseq_1,t3_subset,e4_9_1_1_1__trees_2,t43_finseq_1]),
    [interesting(0.35),file(trees_2,e5_9_1_1_1__trees_2),[file(trees_2,e5_9_1_1_1__trees_2)]]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e6_9_1_1_1__trees_2,plain,(
    r1_tarski(k2_relat_1(c1_9_1_1_1__trees_2),k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_finset_1,cc1_relat_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc11_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,cc1_finseq_1,cc1_nat_1,cc2_nat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_finseq_1,reflexivity_r1_tarski,redefinition_k5_numbers,redefinition_k5_relset_1,dt_k2_relat_1,dt_k5_numbers,dt_k5_relset_1,dt_c1_9_1__trees_2,dt_c1_9_1_1_1__trees_2,t3_subset,e5_9_1_1_1__trees_2,t1_xboole_1]),
    [interesting(0.35),file(trees_2,e6_9_1_1_1__trees_2),[file(trees_2,e6_9_1_1_1__trees_2)]]).

fof(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,d4_finseq_1)]).

fof(e7_9_1_1_1__trees_2,plain,(
    m2_finseq_1(c1_9_1_1_1__trees_2,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finset_1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc4_subset_1,fc6_relat_1,fc8_relat_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_relset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k2_relat_1,dt_k5_numbers,dt_m1_finseq_1,dt_m2_finseq_1,dt_c1_9_1_1_1__trees_2,cc1_finseq_1,rc1_finseq_1,t3_subset,e6_9_1_1_1__trees_2,d4_finseq_1]),
    [interesting(0.35),file(trees_2,e7_9_1_1_1__trees_2),[file(trees_2,e7_9_1_1_1__trees_2)]]).

fof(dt_c2_9_1_1_1__trees_2,plain,(
    m2_finseq_1(c2_9_1_1_1__trees_2,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finset_1,cc1_relat_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,fc4_subset_1,rc1_finset_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_nat_1,cc2_nat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_finseq_1,t3_subset,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_c1_9_1_1_1__trees_2,de_c2_9_1_1_1__trees_2,e7_9_1_1_1__trees_2]),
    [interesting(0.35),file(trees_2,c2_9_1_1_1__trees_2),[file(trees_2,c2_9_1_1_1__trees_2)]]).

fof(de_c3_9_1_1_1__trees_2,definition,(
    c3_9_1_1_1__trees_2 = c2_9_1_1_1__trees_2 ),
    introduced(definition,[new_symbol(c3_9_1_1_1__trees_2),file(trees_2,c3_9_1_1_1__trees_2)]),
    [interesting(0.35),axiom,file(trees_2,c3_9_1_1_1__trees_2)]).

fof(dt_c3_9_1_1_1__trees_2,plain,(
    m2_finseq_1(c3_9_1_1_1__trees_2,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[rc2_finset_1,rc3_finseq_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_finset_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finset_1,rc2_finseq_1,rc2_xreal_0,rc3_finset_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_finset_1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_finseq_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc3_nat_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_c1_9_1_1_1__trees_2,cc1_nat_1,cc2_nat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,t3_subset,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_c2_9_1_1_1__trees_2,de_c2_9_1_1_1__trees_2,de_c3_9_1_1_1__trees_2]),
    [interesting(0.35),file(trees_2,c3_9_1_1_1__trees_2),[file(trees_2,c3_9_1_1_1__trees_2)]]).

fof(d9_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( r2_hidden(B,A)
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_trees_1(C) )
               => ( C = k4_trees_1(A,B)
                <=> ! [D] : 
                      ( m2_finseq_1(D,k5_numbers)
                     => ( r2_hidden(D,C)
                      <=> r2_hidden(k8_finseq_1(k5_numbers,B,D),A) ) ) ) ) ) ) ) ),
    file(trees_1,d9_trees_1),
    [interesting(0.9),axiom,file(trees_1,d9_trees_1)]).

fof(e8_9_1_1_1__trees_2,plain,
    ( r2_hidden(c3_9_1_1_1__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))
    & c1_9_1__trees_2 = k8_finseq_1(k5_numbers,c2_9__trees_2,c3_9_1_1_1__trees_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__trees_2,e1_9__trees_2,e1_9_1_1__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc4_subset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_subset_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_m1_subset_1,dt_m2_relset_1,dt_c2_9_1_1_1__trees_2,de_c2_9_1_1_1__trees_2,cc1_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_relat_1,fc13_finseq_1,fc14_finseq_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_trees_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k4_trees_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c1_9_1_1_1__trees_2,dt_c2_9__trees_2,dt_c3_9_1_1_1__trees_2,de_c3_9_1_1_1__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,e1_9__trees_2,e1_9_1_1__trees_2,e4_9_1_1_1__trees_2,d9_trees_1]),
    [interesting(0.35),file(trees_2,e8_9_1_1_1__trees_2),[file(trees_2,e8_9_1_1_1__trees_2)]]).

fof(i3_9_1_1_1__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i3_9_1_1_1__trees_2)]),
    [interesting(0.35),trivial,file(trees_2,i3_9_1_1_1__trees_2)]).

fof(i2_9_1_1_1__trees_2,plain,
    ( r2_hidden(c3_9_1_1_1__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))
    & c1_9_1__trees_2 = k8_finseq_1(k5_numbers,c2_9__trees_2,c3_9_1_1_1__trees_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__trees_2,e1_9__trees_2,e1_9_1_1__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[e8_9_1_1_1__trees_2,i3_9_1_1_1__trees_2]),
    [interesting(0.35),file(trees_2,i2_9_1_1_1__trees_2),[file(trees_2,i2_9_1_1_1__trees_2)]]).

fof(i1_9_1_1_1__trees_2,plain,(
    ? [A] : 
      ( m2_finseq_1(A,k5_numbers)
      & r2_hidden(A,k4_trees_1(c1_9__trees_2,c2_9__trees_2))
      & c1_9_1__trees_2 = k8_finseq_1(k5_numbers,c2_9__trees_2,A) ) ),
    inference(take,[status(thm),assumptions([dt_c1_9__trees_2,e1_9__trees_2,e1_9_1_1__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9_1_1_1__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_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,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_trees_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,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,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,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k4_trees_1,dt_k5_numbers,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,dt_c3_9_1_1_1__trees_2,i2_9_1_1_1__trees_2]),
    [interesting(0.35),file(trees_2,i1_9_1_1_1__trees_2),[file(trees_2,i1_9_1_1_1__trees_2)]]).

fof(e2_9_1_1__trees_2,plain,(
    ~ ( r2_xboole_0(c2_9__trees_2,c1_9_1__trees_2)
      & ! [A] : 
          ( m2_finseq_1(A,k5_numbers)
         => ~ ( r2_hidden(A,k4_trees_1(c1_9__trees_2,c2_9__trees_2))
              & c1_9_1__trees_2 = k8_finseq_1(k5_numbers,c2_9__trees_2,A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__trees_2,e1_9__trees_2,e1_9_1_1__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2]),discharge_asm(discharge,[e1_9_1_1_1__trees_2])],[e1_9_1_1_1__trees_2,i1_9_1_1_1__trees_2]),
    [interesting(0.5),file(trees_2,e2_9_1_1__trees_2),[file(trees_2,e2_9_1_1__trees_2)]]).

fof(d12_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( r2_hidden(B,A)
               => ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_trees_1(D) )
                   => ( D = k5_trees_1(A,B,C)
                    <=> ! [E] : 
                          ( m2_finseq_1(E,k5_numbers)
                         => ( r2_hidden(E,D)
                          <=> ~ ( ~ ( r2_hidden(E,A)
                                    & ~ r2_xboole_0(B,E) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ~ ( r2_hidden(F,C)
                                        & E = k8_finseq_1(k5_numbers,B,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_1,d12_trees_1),
    [interesting(0.9),axiom,file(trees_1,d12_trees_1)]).

fof(e3_9_1_1__trees_2,plain,(
    r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2,e1_9_1_1__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc4_subset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_relat_1,fc13_finseq_1,fc14_finseq_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_trees_1,fc1_xboole_0,fc2_finseq_1,fc2_trees_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k4_trees_1,dt_k5_numbers,dt_k5_trees_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,e2_9_1_1__trees_2,e1_9__trees_2,e1_9_1_1__trees_2,d12_trees_1]),
    [interesting(0.5),file(trees_2,e3_9_1_1__trees_2),[file(trees_2,e3_9_1_1__trees_2)]]).

fof(i2_9_1_1__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i2_9_1_1__trees_2)]),
    [interesting(0.5),trivial,file(trees_2,i2_9_1_1__trees_2)]).

fof(i1_9_1_1__trees_2,plain,(
    r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2,e1_9_1_1__trees_2])],[e3_9_1_1__trees_2,i2_9_1_1__trees_2]),
    [interesting(0.5),file(trees_2,i1_9_1_1__trees_2),[file(trees_2,i1_9_1_1__trees_2)]]).

fof(e1_9_1__trees_2,plain,
    ( r2_hidden(c1_9_1__trees_2,c1_9__trees_2)
   => r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2]),discharge_asm(discharge,[e1_9_1_1__trees_2])],[e1_9_1_1__trees_2,i1_9_1_1__trees_2]),
    [interesting(0.65),file(trees_2,e1_9_1__trees_2),[file(trees_2,e1_9_1__trees_2)]]).

fof(e2_9_1__trees_2,assumption,
    ( r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
    & ~ r2_hidden(c1_9_1__trees_2,c1_9__trees_2) ),
    introduced(assumption,[file(trees_2,e2_9_1__trees_2)]),
    [interesting(0.65),axiom,file(trees_2,e2_9_1__trees_2)]).

fof(e3_9_1__trees_2,plain,(
    ? [A] : 
      ( m2_finseq_1(A,k5_numbers)
      & r2_hidden(A,k4_trees_1(c1_9__trees_2,c2_9__trees_2))
      & c1_9_1__trees_2 = k8_finseq_1(k5_numbers,c2_9__trees_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e2_9_1__trees_2,e1_9__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc4_subset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_relat_1,fc13_finseq_1,fc14_finseq_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_trees_1,fc1_xboole_0,fc2_finseq_1,fc2_trees_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,irreflexivity_r2_xboole_0,antisymmetry_r2_xboole_0,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k4_trees_1,dt_k5_numbers,dt_k5_trees_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,e2_9_1__trees_2,e1_9__trees_2,d12_trees_1]),
    [interesting(0.65),file(trees_2,e3_9_1__trees_2),[file(trees_2,e3_9_1__trees_2)]]).

fof(e4_9_1__trees_2,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2,e2_9_1__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc4_subset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_relat_1,fc13_finseq_1,fc14_finseq_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_trees_1,fc1_xboole_0,fc2_finseq_1,fc2_trees_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k4_trees_1,dt_k5_numbers,dt_k5_trees_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,e3_9_1__trees_2,e1_9__trees_2,e2_9_1__trees_2,d9_trees_1]),
    [interesting(0.65),file(trees_2,e4_9_1__trees_2),[file(trees_2,e4_9_1__trees_2)]]).

fof(i4_9_1__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i4_9_1__trees_2)]),
    [interesting(0.65),trivial,file(trees_2,i4_9_1__trees_2)]).

fof(i3_9_1__trees_2,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2,e2_9_1__trees_2])],[e4_9_1__trees_2,i4_9_1__trees_2]),
    [interesting(0.65),file(trees_2,i3_9_1__trees_2),[file(trees_2,i3_9_1__trees_2)]]).

fof(i2_9_1__trees_2,plain,(
    ~ ( r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
      & ~ r2_hidden(c1_9_1__trees_2,c1_9__trees_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2]),discharge_asm(discharge,[e2_9_1__trees_2])],[e2_9_1__trees_2,i3_9_1__trees_2]),
    [interesting(0.65),file(trees_2,i2_9_1__trees_2),[file(trees_2,i2_9_1__trees_2)]]).

fof(i1_9_1__trees_2,plain,
    ( ( r2_hidden(c1_9_1__trees_2,c1_9__trees_2)
     => r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) )
    & ~ ( r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
        & ~ r2_hidden(c1_9_1__trees_2,c1_9__trees_2) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__trees_2,dt_c1_9_1__trees_2,dt_c2_9__trees_2,e1_9__trees_2])],[e1_9_1__trees_2,i2_9_1__trees_2]),
    [interesting(0.65),file(trees_2,i1_9_1__trees_2),[file(trees_2,i1_9_1__trees_2)]]).

fof(i1_9_1_tmp__trees_2,plain,
    ( m2_finseq_1(c1_9_1__trees_2,k5_numbers)
   => ( ( r2_hidden(c1_9_1__trees_2,c1_9__trees_2)
       => r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) )
      & ~ ( r2_hidden(c1_9_1__trees_2,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
          & ~ r2_hidden(c1_9_1__trees_2,c1_9__trees_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__trees_2,dt_c2_9__trees_2,e1_9__trees_2]),discharge_asm(discharge,[dt_c1_9_1__trees_2])],[dt_c1_9_1__trees_2,i1_9_1__trees_2]),
    [interesting(0.8),e2_9__trees_2]).

fof(e2_9__trees_2,plain,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ( ( r2_hidden(A,c1_9__trees_2)
         => r2_hidden(A,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2))) )
        & ~ ( r2_hidden(A,k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)))
            & ~ r2_hidden(A,c1_9__trees_2) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__trees_2,dt_c2_9__trees_2,e1_9__trees_2])],[i1_9_1_tmp__trees_2,dh_c1_9_1__trees_2]),
    [interesting(0.8),file(trees_2,e2_9__trees_2),[file(trees_2,e2_9__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 ) ) ) ),
    file(trees_2,t7_trees_2),
    [interesting(0.9),axiom,file(trees_2,t7_trees_2)]).

fof(e3_9__trees_2,plain,(
    c1_9__trees_2 = k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__trees_2,dt_c2_9__trees_2,e1_9__trees_2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc4_subset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc3_finseq_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc6_finseq_1,existence_m1_finseq_1,existence_m1_subset_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_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_relat_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_trees_1,fc1_xboole_0,fc2_finseq_1,fc2_trees_1,fc4_relat_1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,rc2_trees_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k4_trees_1,dt_k5_numbers,dt_k5_trees_1,dt_m2_finseq_1,dt_c1_9__trees_2,dt_c2_9__trees_2,cc1_finset_1,cc1_relat_1,rc1_trees_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,e2_9__trees_2,t7_trees_2]),
    [interesting(0.8),file(trees_2,e3_9__trees_2),[file(trees_2,e3_9__trees_2)]]).

fof(i4_9__trees_2,theorem,(
    $true ),
    introduced(tautology,[file(trees_2,i4_9__trees_2)]),
    [interesting(0.8),trivial,file(trees_2,i4_9__trees_2)]).

fof(i3_9__trees_2,plain,(
    c1_9__trees_2 = k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__trees_2,dt_c2_9__trees_2,e1_9__trees_2])],[e3_9__trees_2,i4_9__trees_2]),
    [interesting(0.8),file(trees_2,i3_9__trees_2),[file(trees_2,i3_9__trees_2)]]).

fof(i2_9__trees_2,plain,
    ( r2_hidden(c2_9__trees_2,c1_9__trees_2)
   => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__trees_2,dt_c2_9__trees_2]),discharge_asm(discharge,[e1_9__trees_2])],[e1_9__trees_2,i3_9__trees_2]),
    [interesting(0.8),file(trees_2,i2_9__trees_2),[file(trees_2,i2_9__trees_2)]]).

fof(i2_9_tmp__trees_2,plain,
    ( m2_finseq_1(c2_9__trees_2,k5_numbers)
   => ( r2_hidden(c2_9__trees_2,c1_9__trees_2)
     => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,c2_9__trees_2,k4_trees_1(c1_9__trees_2,c2_9__trees_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__trees_2]),discharge_asm(discharge,[dt_c2_9__trees_2])],[dt_c2_9__trees_2,i2_9__trees_2]),
    [interesting(0.8),i1_9__trees_2]).

fof(i1_9__trees_2,plain,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ( r2_hidden(A,c1_9__trees_2)
       => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,A,k4_trees_1(c1_9__trees_2,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__trees_2])],[i2_9_tmp__trees_2,dh_c2_9__trees_2]),
    [interesting(0.8),file(trees_2,i1_9__trees_2),[file(trees_2,i1_9__trees_2)]]).

fof(i1_9_tmp__trees_2,plain,
    ( ( ~ v1_xboole_0(c1_9__trees_2)
      & v1_trees_1(c1_9__trees_2) )
   => ! [A] : 
        ( m2_finseq_1(A,k5_numbers)
       => ( r2_hidden(A,c1_9__trees_2)
         => c1_9__trees_2 = k5_trees_1(c1_9__trees_2,A,k4_trees_1(c1_9__trees_2,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_9__trees_2])],[dt_c1_9__trees_2,i1_9__trees_2]),
    [interesting(1),t8_trees_2]).

fof(t8_trees_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( r2_hidden(B,A)
           => A = k5_trees_1(A,B,k4_trees_1(A,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_9_tmp__trees_2,dh_c1_9__trees_2]),
    [interesting(1),file(trees_2,t8_trees_2),[file(trees_2,t8_trees_2)]]).