% Mizar ND problem: t3_bintree2,bintree2,98,15 
fof(dh_c1_4__bintree2,definition,
    ( ( ( ~ v1_xboole_0(c1_4__bintree2)
        & v1_trees_1(c1_4__bintree2) )
     => ( c1_4__bintree2 = k3_finseq_2(k7_domain_1(k5_numbers,0,1))
       => v1_bintree1(c1_4__bintree2) ) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & v1_trees_1(A) )
       => ( A = k3_finseq_2(k7_domain_1(k5_numbers,0,1))
         => v1_bintree1(A) ) ) ),
    introduced(definition,[new_symbol(c1_4__bintree2),file(bintree2,c1_4__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c1_4__bintree2)]).

fof(e1_4__bintree2,assumption,(
    c1_4__bintree2 = k3_finseq_2(k7_domain_1(k5_numbers,0,1)) ),
    introduced(assumption,[file(bintree2,e1_4__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,e1_4__bintree2)]).

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_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

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

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

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

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

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

fof(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(fc4_trees_9,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v2_trees_9(A)
        & m1_subset_1(B,A) )
     => v1_finset_1(k1_trees_2(A,B)) ) ),
    file(trees_9,fc4_trees_9),
    [interesting(0.9),axiom,file(trees_9,fc4_trees_9)]).

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_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

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_finset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]).

fof(rc2_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_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_trees_9,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_1(A)
      & v1_trees_2(A)
      & v2_trees_9(A) ) ),
    file(trees_9,rc3_trees_9),
    [interesting(0.9),axiom,file(trees_9,rc3_trees_9)]).

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

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

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

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

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc6_trees_9,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_finseq_1(B) ) ) ),
    file(trees_9,rc6_trees_9),
    [interesting(0.9),axiom,file(trees_9,rc6_trees_9)]).

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_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_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k4_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(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(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_trees_9,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A) ) ) ),
    file(trees_9,cc1_trees_9),
    [interesting(0.9),axiom,file(trees_9,cc1_trees_9)]).

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(cc3_trees_9,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A) )
     => ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v2_trees_9(A) ) ) ),
    file(trees_9,cc3_trees_9),
    [interesting(0.9),axiom,file(trees_9,cc3_trees_9)]).

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(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]).

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

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

fof(fc1_trees_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A)
        & m1_subset_1(B,A) )
     => v1_finset_1(k1_trees_2(A,B)) ) ),
    file(trees_2,fc1_trees_2),
    [interesting(0.9),axiom,file(trees_2,fc1_trees_2)]).

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(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(rc1_bintree1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_1(A)
      & v1_bintree1(A) ) ),
    file(bintree1,rc1_bintree1),
    [interesting(0.9),axiom,file(bintree1,rc1_bintree1)]).

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_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc1_trees_2,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_trees_1(A)
      & v1_trees_2(A) ) ),
    file(trees_2,rc1_trees_2),
    [interesting(0.9),axiom,file(trees_2,rc1_trees_2)]).

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

fof(rc3_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(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(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(commutativity_k7_domain_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k7_domain_1(A,B,C) = k7_domain_1(A,C,B) ) ),
    file(domain_1,k7_domain_1),
    [interesting(0.9),axiom,file(domain_1,k7_domain_1)]).

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

fof(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_k13_binarith,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k13_binarith(A,B) = k5_finseq_1(B) ) ),
    file(binarith,k13_binarith),
    [interesting(0.9),axiom,file(binarith,k13_binarith)]).

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_k7_domain_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k7_domain_1(A,B,C) = k2_tarski(B,C) ) ),
    file(domain_1,k7_domain_1),
    [interesting(0.9),axiom,file(domain_1,k7_domain_1)]).

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_k13_binarith,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m2_finseq_2(k13_binarith(A,B),A,k4_finseq_2(1,A)) ) ),
    file(binarith,k13_binarith),
    [interesting(0.9),axiom,file(binarith,k13_binarith)]).

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

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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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_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_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(domain_1,k7_domain_1),
    [interesting(0.9),axiom,file(domain_1,k7_domain_1)]).

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_4__bintree2,assumption,
    ( ~ v1_xboole_0(c1_4__bintree2)
    & v1_trees_1(c1_4__bintree2) ),
    introduced(assumption,[file(bintree2,c1_4__bintree2)]),
    [interesting(0.8),axiom,file(bintree2,c1_4__bintree2)]).

fof(cc1_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_bintree1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A) ) ) ),
    file(bintree1,cc1_bintree1),
    [interesting(0.9),axiom,file(bintree1,cc1_bintree1)]).

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(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_finset_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_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(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_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(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(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(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(dh_c1_4_1__bintree2,definition,
    ( ( m1_trees_1(c1_4_1__bintree2,c1_4__bintree2)
     => ( ~ r2_hidden(c1_4_1__bintree2,k3_trees_1(c1_4__bintree2))
       => k1_trees_2(c1_4__bintree2,c1_4_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))) ) )
   => ! [A] : 
        ( m1_trees_1(A,c1_4__bintree2)
       => ( ~ r2_hidden(A,k3_trees_1(c1_4__bintree2))
         => k1_trees_2(c1_4__bintree2,A) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,A,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,A,k13_binarith(k5_numbers,1))) ) ) ),
    introduced(definition,[new_symbol(c1_4_1__bintree2),file(bintree2,c1_4_1__bintree2)]),
    [interesting(0.65),axiom,file(bintree2,c1_4_1__bintree2)]).

fof(e1_4_1__bintree2,assumption,(
    ~ r2_hidden(c1_4_1__bintree2,k3_trees_1(c1_4__bintree2)) ),
    introduced(assumption,[file(bintree2,e1_4_1__bintree2)]),
    [interesting(0.65),axiom,file(bintree2,e1_4_1__bintree2)]).

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(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_c1_4_1__bintree2,assumption,(
    m1_trees_1(c1_4_1__bintree2,c1_4__bintree2) ),
    introduced(assumption,[file(bintree2,c1_4_1__bintree2)]),
    [interesting(0.65),axiom,file(bintree2,c1_4_1__bintree2)]).

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_1_bintree2,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_trees_1(B)
        & m1_trees_1(C,B) )
     => ( r2_hidden(A,a_2_1_bintree2(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k8_finseq_1(k5_numbers,C,k13_binarith(k5_numbers,D))
            & r2_hidden(k8_finseq_1(k5_numbers,C,k13_binarith(k5_numbers,D)),B) ) ) ) ),
    file(bintree2,a_2_1_bintree2),
    [interesting(0.9),axiom,file(bintree2,a_2_1_bintree2)]).

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

fof(dt_c1_4_1_1_1__bintree2,assumption,(
    $true ),
    introduced(assumption,[file(bintree2,c1_4_1_1_1__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c1_4_1_1_1__bintree2)]).

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

fof(dh_c1_4_1_1_1__bintree2,definition,
    ( ~ ( r2_hidden(c1_4_1_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2))
        & ~ r2_hidden(c1_4_1_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) )
   => ! [A] : 
        ~ ( r2_hidden(A,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2))
          & ~ r2_hidden(A,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ) ),
    introduced(definition,[new_symbol(c1_4_1_1_1__bintree2),file(bintree2,c1_4_1_1_1__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c1_4_1_1_1__bintree2)]).

fof(e1_4_1_1_1__bintree2,assumption,(
    r2_hidden(c1_4_1_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ),
    introduced(assumption,[file(bintree2,e1_4_1_1_1__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,e1_4_1_1_1__bintree2)]).

fof(dh_c2_4_1_1_1__bintree2,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & c1_4_1_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,A))
        & r2_hidden(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,A)),c1_4__bintree2) )
   => ( m2_subset_1(c2_4_1_1_1__bintree2,k1_numbers,k5_numbers)
      & c1_4_1_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2))
      & r2_hidden(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)),c1_4__bintree2) ) ),
    introduced(definition,[new_symbol(c2_4_1_1_1__bintree2),file(bintree2,c2_4_1_1_1__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c2_4_1_1_1__bintree2)]).

fof(e2_4_1_1_1__bintree2,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & c1_4_1_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,A))
      & r2_hidden(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,A)),c1_4__bintree2) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[rc3_trees_9,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_trees_9,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc2_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,spc1_boole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,spc1_numerals,spc1_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_subset_1,dt_k13_binarith,dt_k1_numbers,dt_k5_numbers,dt_k8_finseq_1,dt_m2_subset_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_1_bintree2,e1_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,e2_4_1_1_1__bintree2),[file(bintree2,e2_4_1_1_1__bintree2)]]).

fof(dt_c2_4_1_1_1__bintree2,plain,(
    m2_subset_1(c2_4_1_1_1__bintree2,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[dh_c2_4_1_1_1__bintree2,e2_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,c2_4_1_1_1__bintree2),[file(bintree2,c2_4_1_1_1__bintree2)]]).

fof(fc10_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]).

fof(fc11_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]).

fof(fc12_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]).

fof(fc1_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]).

fof(fc3_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]).

fof(fc3_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]).

fof(fc4_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]).

fof(fc7_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]).

fof(fc8_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]).

fof(fc9_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]).

fof(spc6_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

fof(t1_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    [interesting(0.9),axiom,file(arithm,t1_arithm)]).

fof(commutativity_k2_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

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

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,(
    k2_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,(
    k2_xcmplx_0(0,1) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,(
    k2_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]).

fof(commutativity_k1_nat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(redefinition_k1_nat_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

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

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

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

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,k4_finseq_4)]).

fof(de_c3_4_1_1_1__bintree2,definition,(
    c3_4_1_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)) ),
    introduced(definition,[new_symbol(c3_4_1_1_1__bintree2),file(bintree2,c3_4_1_1_1__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c3_4_1_1_1__bintree2)]).

fof(e4_4_1_1_1__bintree2,plain,(
    r2_hidden(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)),c1_4__bintree2) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[dh_c2_4_1_1_1__bintree2,e2_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,e4_4_1_1_1__bintree2),[file(bintree2,e4_4_1_1_1__bintree2)]]).

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

fof(e5_4_1_1_1__bintree2,plain,(
    m2_finseq_1(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)),k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k13_binarith,dt_k13_finseq_1,dt_k3_finseq_2,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c2_4_1_1_1__bintree2,fc16_finseq_1,fc9_finseq_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_4__bintree2,e4_4_1_1_1__bintree2,d11_finseq_1]),
    [interesting(0.35),file(bintree2,e5_4_1_1_1__bintree2),[file(bintree2,e5_4_1_1_1__bintree2)]]).

fof(dt_c3_4_1_1_1__bintree2,plain,(
    m2_finseq_1(c3_4_1_1_1__bintree2,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k7_domain_1,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m2_finseq_1,dt_k13_binarith,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_c1_4_1__bintree2,dt_c2_4_1_1_1__bintree2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,de_c3_4_1_1_1__bintree2,e5_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,c3_4_1_1_1__bintree2),[file(bintree2,c3_4_1_1_1__bintree2)]]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(fc5_trees_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(trees_2,fc5_trees_2),
    [interesting(0.9),axiom,file(trees_2,fc5_trees_2)]).

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

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

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

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

fof(fc1_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]).

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

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

fof(redefinition_k9_finseq_1,definition,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

fof(dt_k9_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k9_finseq_1(A))
      & v1_funct_1(k9_finseq_1(A)) ) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

fof(t6_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ),
    file(finseq_1,t6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t6_finseq_1)]).

fof(e6_4_1_1_1__bintree2,plain,(
    r2_hidden(k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1),k2_finseq_1(k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc3_trees_9,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m2_finseq_1,cc1_trees_9,cc2_finset_1,fc1_margrel1,fc1_ordinal2,fc2_finseq_1,rc1_finset_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_finseq_1,fc1_subset_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k1_nat_1,dt_k2_finseq_1,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_c1_4_1__bintree2,cc1_xreal_0,cc3_nat_1,fc1_nat_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,t6_finseq_1]),
    [interesting(0.35),file(bintree2,e6_4_1_1_1__bintree2),[file(bintree2,e6_4_1_1_1__bintree2)]]).

fof(t19_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),1) ) ),
    file(finseq_2,t19_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,t19_finseq_2)]).

fof(e7_4_1_1_1__bintree2,plain,(
    r2_hidden(k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1),k2_finseq_1(k3_finseq_1(c3_4_1_1_1__bintree2))) ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2])],[rc3_trees_9,existence_m1_finseq_2,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_relset_1,cc3_trees_9,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_tarski,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_trees_9,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_margrel1,fc1_ordinal2,fc2_finseq_1,fc2_finset_1,fc3_subset_1,fc3_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_arithm,commutativity_k2_xcmplx_0,commutativity_k7_domain_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k13_binarith,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finseq_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_4__bintree2,dt_c2_4_1_1_1__bintree2,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc3_nat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_finseq_1,fc1_nat_1,fc1_subset_1,fc3_finseq_1,fc3_nat_1,fc4_finseq_1,fc4_nat_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc0_boole,spc0_numerals,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,spc0_numerals,spc0_boole,commutativity_k1_nat_1,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k9_finseq_1,dt_k1_nat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k7_finseq_1,dt_k9_finseq_1,dt_c1_4_1__bintree2,dt_c3_4_1_1_1__bintree2,de_c3_4_1_1_1__bintree2,cc1_finseq_1,rc1_finseq_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e6_4_1_1_1__bintree2,t19_finseq_2]),
    [interesting(0.35),file(bintree2,e7_4_1_1_1__bintree2),[file(bintree2,e7_4_1_1_1__bintree2)]]).

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

fof(e8_4_1_1_1__bintree2,plain,(
    r2_hidden(k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1),k4_finseq_1(c3_4_1_1_1__bintree2)) ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2])],[rc3_trees_9,existence_m1_finseq_2,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_relset_1,cc3_trees_9,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_trees_9,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_finseq_1,fc12_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc2_finseq_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc3_xreal_0,fc4_finseq_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_arithm,commutativity_k2_xcmplx_0,commutativity_k7_domain_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,dt_k13_binarith,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_c1_4__bintree2,dt_c2_4_1_1_1__bintree2,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc3_nat_1,fc17_finseq_1,fc1_finseq_1,fc1_nat_1,fc1_ordinal2,fc1_subset_1,fc3_nat_1,fc4_nat_1,fc5_trees_2,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc0_boole,spc0_numerals,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,spc0_numerals,spc0_boole,commutativity_k1_nat_1,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_4_1__bintree2,dt_c3_4_1_1_1__bintree2,de_c3_4_1_1_1__bintree2,cc1_finseq_1,rc1_finseq_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e7_4_1_1_1__bintree2,d3_finseq_1]),
    [interesting(0.35),file(bintree2,e8_4_1_1_1__bintree2),[file(bintree2,e8_4_1_1_1__bintree2)]]).

fof(d4_finseq_4,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,d4_finseq_4)]).

fof(e1_4_1_1_1_1__bintree2,plain,(
    k4_finseq_4(k5_numbers,k7_domain_1(k5_numbers,0,1),c3_4_1_1_1__bintree2,k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1)) = k1_funct_1(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)),k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1)) ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m1_finseq_2,dt_k1_xboole_0,dt_m1_finseq_2,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_finset_1,fc17_finseq_1,fc1_margrel1,fc1_nat_1,fc2_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc5_trees_2,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,spc6_arithm,t1_arithm,commutativity_k2_tarski,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc2_nat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc9_trees_2,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k13_binarith,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m2_relset_1,dt_k13_binarith,dt_k1_funct_1,dt_k1_nat_1,dt_k1_relat_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m2_relset_1,dt_c1_4_1__bintree2,dt_c2_4_1_1_1__bintree2,dt_c3_4_1_1_1__bintree2,de_c3_4_1_1_1__bintree2,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e8_4_1_1_1__bintree2,d4_finseq_4]),
    [interesting(0.2),file(bintree2,e1_4_1_1_1_1__bintree2),[file(bintree2,e1_4_1_1_1_1__bintree2)]]).

fof(t59_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A ) ),
    file(finseq_1,t59_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t59_finseq_1)]).

fof(e2_4_1_1_1_1__bintree2,plain,(
    k1_funct_1(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)),k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1)) = c2_4_1_1_1__bintree2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[rc3_trees_9,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_trees_9,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_trees_9,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_margrel1,fc1_nat_1,fc2_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,redefinition_k13_binarith,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_k9_finseq_1,dt_k13_binarith,dt_k1_funct_1,dt_k1_nat_1,dt_k3_finseq_1,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_k9_finseq_1,dt_c1_4_1__bintree2,dt_c2_4_1_1_1__bintree2,cc1_finseq_1,rc1_finseq_1,spc1_numerals,spc1_boole,t59_finseq_1]),
    [interesting(0.2),file(bintree2,e2_4_1_1_1_1__bintree2),[file(bintree2,e2_4_1_1_1_1__bintree2)]]).

fof(e9_4_1_1_1__bintree2,plain,(
    k4_finseq_4(k5_numbers,k7_domain_1(k5_numbers,0,1),c3_4_1_1_1__bintree2,k1_nat_1(k3_finseq_1(c1_4_1__bintree2),1)) = c2_4_1_1_1__bintree2 ),
    inference(iterative_eq,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[e1_4_1_1_1_1__bintree2,e2_4_1_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,e9_4_1_1_1__bintree2),[file(bintree2,e9_4_1_1_1__bintree2)]]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.9),axiom,file(tarski,d2_tarski)]).

fof(e10_4_1_1_1__bintree2,plain,
    ( c2_4_1_1_1__bintree2 = 0
    | c2_4_1_1_1__bintree2 = 1 ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[rc3_trees_9,existence_m1_finseq_2,dt_k2_zfmisc_1,dt_m1_finseq_2,cc1_relset_1,cc3_trees_9,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k4_finseq_2,dt_k5_finseq_1,dt_k7_finseq_1,dt_m1_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_trees_9,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_finseq_1,fc12_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc1_nat_1,fc2_finseq_1,fc3_finseq_1,fc3_nat_1,fc3_xreal_0,fc4_finseq_1,fc4_nat_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_arithm,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k13_binarith,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k13_binarith,dt_k1_card_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_k8_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finseq_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finseq_1,rc1_finset_1,rc1_subset_1,rc2_finseq_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_k7_domain_1,dt_k1_nat_1,dt_k2_tarski,dt_k3_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_k7_domain_1,dt_c1_4_1__bintree2,dt_c2_4_1_1_1__bintree2,dt_c3_4_1_1_1__bintree2,de_c3_4_1_1_1__bintree2,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_4_1_1_1__bintree2,d2_tarski]),
    [interesting(0.35),file(bintree2,e10_4_1_1_1__bintree2),[file(bintree2,e10_4_1_1_1__bintree2)]]).

fof(e3_4_1_1_1__bintree2,plain,(
    c1_4_1_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,c2_4_1_1_1__bintree2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[dh_c2_4_1_1_1__bintree2,e2_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,e3_4_1_1_1__bintree2),[file(bintree2,e3_4_1_1_1__bintree2)]]).

fof(e11_4_1_1_1__bintree2,plain,(
    r2_hidden(c1_4_1_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ),
    inference(mizar_by,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[rc3_trees_9,existence_m1_relset_1,dt_m1_relset_1,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc2_finseq_1,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc14_finset_1,fc1_ordinal2,fc3_finseq_1,fc4_finseq_1,fc4_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,dt_k13_binarith,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,dt_c2_4_1_1_1__bintree2,fc1_subset_1,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e10_4_1_1_1__bintree2,e3_4_1_1_1__bintree2,d2_tarski]),
    [interesting(0.35),file(bintree2,e11_4_1_1_1__bintree2),[file(bintree2,e11_4_1_1_1__bintree2)]]).

fof(i3_4_1_1_1__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i3_4_1_1_1__bintree2)]),
    [interesting(0.35),trivial,file(bintree2,i3_4_1_1_1__bintree2)]).

fof(i2_4_1_1_1__bintree2,plain,(
    r2_hidden(c1_4_1_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ),
    inference(conclusion,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2,e1_4_1_1_1__bintree2])],[e11_4_1_1_1__bintree2,i3_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,i2_4_1_1_1__bintree2),[file(bintree2,i2_4_1_1_1__bintree2)]]).

fof(i1_4_1_1_1__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2))
      & ~ r2_hidden(c1_4_1_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1_1__bintree2]),discharge_asm(discharge,[e1_4_1_1_1__bintree2])],[e1_4_1_1_1__bintree2,i2_4_1_1_1__bintree2]),
    [interesting(0.35),file(bintree2,i1_4_1_1_1__bintree2),[file(bintree2,i1_4_1_1_1__bintree2)]]).

fof(i1_4_1_1_1_tmp__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2))
      & ~ r2_hidden(c1_4_1_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2]),discharge_asm(discharge,[dt_c1_4_1_1_1__bintree2])],[dt_c1_4_1_1_1__bintree2,i1_4_1_1_1__bintree2]),
    [interesting(0.5),e1_4_1_1__bintree2]).

fof(e1_4_1_1__bintree2,plain,(
    r1_tarski(a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2),k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ),
    inference(let,[status(thm),assumptions([e1_4__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2])],[i1_4_1_1_1_tmp__bintree2,rc3_trees_9,dt_m1_relset_1,cc3_trees_9,rc1_trees_2,rc2_finseq_1,rc9_trees_2,redefinition_m2_relset_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,commutativity_k7_domain_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,dt_k13_binarith,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,fc1_subset_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t2_tarski,fraenkel_a_2_1_bintree2,d3_tarski,dh_c1_4_1_1_1__bintree2]),
    [interesting(0.5),file(bintree2,e1_4_1_1__bintree2),[file(bintree2,e1_4_1_1__bintree2)]]).

fof(dt_c1_4_1_1__bintree2,assumption,(
    $true ),
    introduced(assumption,[file(bintree2,c1_4_1_1__bintree2)]),
    [interesting(0.5),axiom,file(bintree2,c1_4_1_1__bintree2)]).

fof(dh_c1_4_1_1__bintree2,definition,
    ( ~ ( r2_hidden(c1_4_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))))
        & ~ r2_hidden(c1_4_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))))
          & ~ r2_hidden(A,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ) ),
    introduced(definition,[new_symbol(c1_4_1_1__bintree2),file(bintree2,c1_4_1_1__bintree2)]),
    [interesting(0.5),axiom,file(bintree2,c1_4_1_1__bintree2)]).

fof(e11_4_1_1__bintree2,assumption,(
    r2_hidden(c1_4_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)))) ),
    introduced(assumption,[file(bintree2,e11_4_1_1__bintree2)]),
    [interesting(0.5),axiom,file(bintree2,e11_4_1_1__bintree2)]).

fof(e12_4_1_1__bintree2,plain,
    ( c1_4_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0))
    | c1_4_1_1__bintree2 = k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1__bintree2,e11_4_1_1__bintree2])],[rc3_trees_9,existence_m1_relset_1,dt_m1_relset_1,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc2_finseq_1,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc14_finset_1,fc1_ordinal2,fc3_finseq_1,fc4_finseq_1,fc4_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,dt_k13_binarith,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_c1_4_1__bintree2,dt_c1_4_1_1__bintree2,fc1_subset_1,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e11_4_1_1__bintree2,d2_tarski]),
    [interesting(0.5),file(bintree2,e12_4_1_1__bintree2),[file(bintree2,e12_4_1_1__bintree2)]]).

fof(existence_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m1_trees_4(C,A,B) ) ),
    file(trees_4,m1_trees_4),
    [interesting(0.9),axiom,file(trees_4,m1_trees_4)]).

fof(redefinition_m1_trees_4,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m1_trees_4(C,A,B)
        <=> m1_finseq_1(C,B) ) ) ),
    file(trees_4,m1_trees_4),
    [interesting(0.9),axiom,file(trees_4,m1_trees_4)]).

fof(dt_m1_trees_4,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m1_trees_4(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(trees_4,m1_trees_4),
    [interesting(0.9),axiom,file(trees_4,m1_trees_4)]).

fof(e2_4_1_1__bintree2,plain,(
    m1_trees_4(c1_4_1__bintree2,k5_numbers,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_subset_1,existence_m1_trees_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_relset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m1_trees_4,existence_m2_finseq_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_m1_trees_4,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k3_finseq_2,dt_k5_numbers,dt_k7_domain_1,dt_m1_trees_4,dt_m2_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,fc16_finseq_1,fc9_finseq_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_4__bintree2,d11_finseq_1]),
    [interesting(0.5),file(bintree2,e2_4_1_1__bintree2),[file(bintree2,e2_4_1_1__bintree2)]]).

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(dt_c1_4_1_1_2__bintree2,assumption,(
    $true ),
    introduced(assumption,[file(bintree2,c1_4_1_1_2__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c1_4_1_1_2__bintree2)]).

fof(dh_c1_4_1_1_2__bintree2,definition,
    ( ~ ( r2_hidden(c1_4_1_1_2__bintree2,k2_relat_1(k13_binarith(k5_numbers,0)))
        & ~ r2_hidden(c1_4_1_1_2__bintree2,k7_domain_1(k5_numbers,0,1)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_relat_1(k13_binarith(k5_numbers,0)))
          & ~ r2_hidden(A,k7_domain_1(k5_numbers,0,1)) ) ),
    introduced(definition,[new_symbol(c1_4_1_1_2__bintree2),file(bintree2,c1_4_1_1_2__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c1_4_1_1_2__bintree2)]).

fof(e1_4_1_1_2__bintree2,assumption,(
    r2_hidden(c1_4_1_1_2__bintree2,k2_relat_1(k13_binarith(k5_numbers,0))) ),
    introduced(assumption,[file(bintree2,e1_4_1_1_2__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,e1_4_1_1_2__bintree2)]).

fof(redefinition_k6_domain_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_1)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_1)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(t55_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t55_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t55_finseq_1)]).

fof(e2_4_1_1_2__bintree2,plain,(
    r2_hidden(c1_4_1_1_2__bintree2,k6_domain_1(k5_numbers,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1_2__bintree2,e1_4_1_1_2__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_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,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc3_nat_1,fc11_finseq_1,fc12_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_trees_2,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k2_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k9_finseq_1,dt_k13_binarith,dt_k1_tarski,dt_k2_finseq_1,dt_k2_relat_1,dt_k4_finseq_1,dt_k5_numbers,dt_k6_domain_1,dt_k9_finseq_1,dt_c1_4_1_1_2__bintree2,cc1_finseq_1,fc1_finset_1,fc2_subset_1,rc1_finseq_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_4_1_1_2__bintree2,t55_finseq_1]),
    [interesting(0.35),file(bintree2,e2_4_1_1_2__bintree2),[file(bintree2,e2_4_1_1_2__bintree2)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e3_4_1_1_2__bintree2,plain,(
    c1_4_1_1_2__bintree2 = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1_2__bintree2,e1_4_1_1_2__bintree2])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k6_domain_1,dt_k1_tarski,dt_k5_numbers,dt_k6_domain_1,dt_c1_4_1_1_2__bintree2,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,spc0_numerals,spc0_boole,e2_4_1_1_2__bintree2,d1_tarski]),
    [interesting(0.35),file(bintree2,e3_4_1_1_2__bintree2),[file(bintree2,e3_4_1_1_2__bintree2)]]).

fof(e4_4_1_1_2__bintree2,plain,(
    r2_hidden(c1_4_1_1_2__bintree2,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1_2__bintree2,e1_4_1_1_2__bintree2])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k7_domain_1,dt_k2_tarski,dt_k5_numbers,dt_k7_domain_1,dt_c1_4_1_1_2__bintree2,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_4_1_1_2__bintree2,d2_tarski]),
    [interesting(0.35),file(bintree2,e4_4_1_1_2__bintree2),[file(bintree2,e4_4_1_1_2__bintree2)]]).

fof(i3_4_1_1_2__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i3_4_1_1_2__bintree2)]),
    [interesting(0.35),trivial,file(bintree2,i3_4_1_1_2__bintree2)]).

fof(i2_4_1_1_2__bintree2,plain,(
    r2_hidden(c1_4_1_1_2__bintree2,k7_domain_1(k5_numbers,0,1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4_1_1_2__bintree2,e1_4_1_1_2__bintree2])],[e4_4_1_1_2__bintree2,i3_4_1_1_2__bintree2]),
    [interesting(0.35),file(bintree2,i2_4_1_1_2__bintree2),[file(bintree2,i2_4_1_1_2__bintree2)]]).

fof(i1_4_1_1_2__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1_2__bintree2,k2_relat_1(k13_binarith(k5_numbers,0)))
      & ~ r2_hidden(c1_4_1_1_2__bintree2,k7_domain_1(k5_numbers,0,1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4_1_1_2__bintree2]),discharge_asm(discharge,[e1_4_1_1_2__bintree2])],[e1_4_1_1_2__bintree2,i2_4_1_1_2__bintree2]),
    [interesting(0.35),file(bintree2,i1_4_1_1_2__bintree2),[file(bintree2,i1_4_1_1_2__bintree2)]]).

fof(i1_4_1_1_2_tmp__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1_2__bintree2,k2_relat_1(k13_binarith(k5_numbers,0)))
      & ~ r2_hidden(c1_4_1_1_2__bintree2,k7_domain_1(k5_numbers,0,1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4_1_1_2__bintree2])],[dt_c1_4_1_1_2__bintree2,i1_4_1_1_2__bintree2]),
    [interesting(0.5),e3_4_1_1__bintree2]).

fof(e3_4_1_1__bintree2,plain,(
    r1_tarski(k2_relat_1(k13_binarith(k5_numbers,0)),k7_domain_1(k5_numbers,0,1)) ),
    inference(let,[status(thm),assumptions([])],[i1_4_1_1_2_tmp__bintree2,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,redefinition_m2_finseq_1,dt_m1_finseq_2,dt_m2_finseq_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc11_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,commutativity_k7_domain_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,dt_k13_binarith,dt_k2_relat_1,dt_k5_numbers,dt_k7_domain_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d3_tarski,dh_c1_4_1_1_2__bintree2]),
    [interesting(0.5),file(bintree2,e3_4_1_1__bintree2),[file(bintree2,e3_4_1_1__bintree2)]]).

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(e4_4_1_1__bintree2,plain,(
    m1_trees_4(k13_binarith(k5_numbers,0),k5_numbers,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc9_trees_2,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k7_domain_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_trees_4,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_m1_trees_4,dt_k13_binarith,dt_k2_relat_1,dt_k5_numbers,dt_k7_domain_1,dt_m1_finseq_1,dt_m1_trees_4,cc1_finseq_1,rc1_finseq_1,t3_subset,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_4_1_1__bintree2,d4_finseq_1]),
    [interesting(0.5),file(bintree2,e4_4_1_1__bintree2),[file(bintree2,e4_4_1_1__bintree2)]]).

fof(t23_scmfsa_7,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ! [C] : 
          ( m2_finseq_1(C,A)
         => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ) ),
    file(scmfsa_7,t23_scmfsa_7),
    [interesting(0.9),axiom,file(scmfsa_7,t23_scmfsa_7)]).

fof(e7_4_1_1__bintree2,plain,(
    m1_trees_4(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k5_numbers,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k7_domain_1,existence_m1_trees_4,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_4,redefinition_m2_finseq_1,dt_k13_binarith,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_trees_4,dt_m2_finseq_1,dt_c1_4_1__bintree2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_4_1_1__bintree2,e4_4_1_1__bintree2,t23_scmfsa_7]),
    [interesting(0.5),file(bintree2,e7_4_1_1__bintree2),[file(bintree2,e7_4_1_1__bintree2)]]).

fof(e8_4_1_1__bintree2,plain,(
    r2_hidden(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),c1_4__bintree2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m1_trees_4,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_4,redefinition_m2_finseq_1,dt_k13_binarith,dt_k13_finseq_1,dt_k3_finseq_2,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_trees_4,dt_m2_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,fc16_finseq_1,fc9_finseq_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e7_4_1_1__bintree2,e1_4__bintree2,d11_finseq_1]),
    [interesting(0.5),file(bintree2,e8_4_1_1__bintree2),[file(bintree2,e8_4_1_1__bintree2)]]).

fof(dt_c1_4_1_1_3__bintree2,assumption,(
    $true ),
    introduced(assumption,[file(bintree2,c1_4_1_1_3__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c1_4_1_1_3__bintree2)]).

fof(dh_c1_4_1_1_3__bintree2,definition,
    ( ~ ( r2_hidden(c1_4_1_1_3__bintree2,k2_relat_1(k13_binarith(k5_numbers,1)))
        & ~ r2_hidden(c1_4_1_1_3__bintree2,k7_domain_1(k5_numbers,0,1)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_relat_1(k13_binarith(k5_numbers,1)))
          & ~ r2_hidden(A,k7_domain_1(k5_numbers,0,1)) ) ),
    introduced(definition,[new_symbol(c1_4_1_1_3__bintree2),file(bintree2,c1_4_1_1_3__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,c1_4_1_1_3__bintree2)]).

fof(e1_4_1_1_3__bintree2,assumption,(
    r2_hidden(c1_4_1_1_3__bintree2,k2_relat_1(k13_binarith(k5_numbers,1))) ),
    introduced(assumption,[file(bintree2,e1_4_1_1_3__bintree2)]),
    [interesting(0.35),axiom,file(bintree2,e1_4_1_1_3__bintree2)]).

fof(e2_4_1_1_3__bintree2,plain,(
    r2_hidden(c1_4_1_1_3__bintree2,k6_domain_1(k5_numbers,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1_3__bintree2,e1_4_1_1_3__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_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,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc3_nat_1,fc11_finseq_1,fc12_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_trees_2,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k2_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k9_finseq_1,dt_k13_binarith,dt_k1_tarski,dt_k2_finseq_1,dt_k2_relat_1,dt_k4_finseq_1,dt_k5_numbers,dt_k6_domain_1,dt_k9_finseq_1,dt_c1_4_1_1_3__bintree2,cc1_finseq_1,fc1_finset_1,fc2_subset_1,rc1_finseq_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e1_4_1_1_3__bintree2,t55_finseq_1]),
    [interesting(0.35),file(bintree2,e2_4_1_1_3__bintree2),[file(bintree2,e2_4_1_1_3__bintree2)]]).

fof(e3_4_1_1_3__bintree2,plain,(
    c1_4_1_1_3__bintree2 = 1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1_3__bintree2,e1_4_1_1_3__bintree2])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k6_domain_1,dt_k1_tarski,dt_k5_numbers,dt_k6_domain_1,dt_c1_4_1_1_3__bintree2,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e2_4_1_1_3__bintree2,d1_tarski]),
    [interesting(0.35),file(bintree2,e3_4_1_1_3__bintree2),[file(bintree2,e3_4_1_1_3__bintree2)]]).

fof(e4_4_1_1_3__bintree2,plain,(
    r2_hidden(c1_4_1_1_3__bintree2,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1_3__bintree2,e1_4_1_1_3__bintree2])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k7_domain_1,dt_k2_tarski,dt_k5_numbers,dt_k7_domain_1,dt_c1_4_1_1_3__bintree2,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_4_1_1_3__bintree2,d2_tarski]),
    [interesting(0.35),file(bintree2,e4_4_1_1_3__bintree2),[file(bintree2,e4_4_1_1_3__bintree2)]]).

fof(i3_4_1_1_3__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i3_4_1_1_3__bintree2)]),
    [interesting(0.35),trivial,file(bintree2,i3_4_1_1_3__bintree2)]).

fof(i2_4_1_1_3__bintree2,plain,(
    r2_hidden(c1_4_1_1_3__bintree2,k7_domain_1(k5_numbers,0,1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4_1_1_3__bintree2,e1_4_1_1_3__bintree2])],[e4_4_1_1_3__bintree2,i3_4_1_1_3__bintree2]),
    [interesting(0.35),file(bintree2,i2_4_1_1_3__bintree2),[file(bintree2,i2_4_1_1_3__bintree2)]]).

fof(i1_4_1_1_3__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1_3__bintree2,k2_relat_1(k13_binarith(k5_numbers,1)))
      & ~ r2_hidden(c1_4_1_1_3__bintree2,k7_domain_1(k5_numbers,0,1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4_1_1_3__bintree2]),discharge_asm(discharge,[e1_4_1_1_3__bintree2])],[e1_4_1_1_3__bintree2,i2_4_1_1_3__bintree2]),
    [interesting(0.35),file(bintree2,i1_4_1_1_3__bintree2),[file(bintree2,i1_4_1_1_3__bintree2)]]).

fof(i1_4_1_1_3_tmp__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1_3__bintree2,k2_relat_1(k13_binarith(k5_numbers,1)))
      & ~ r2_hidden(c1_4_1_1_3__bintree2,k7_domain_1(k5_numbers,0,1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4_1_1_3__bintree2])],[dt_c1_4_1_1_3__bintree2,i1_4_1_1_3__bintree2]),
    [interesting(0.5),e5_4_1_1__bintree2]).

fof(e5_4_1_1__bintree2,plain,(
    r1_tarski(k2_relat_1(k13_binarith(k5_numbers,1)),k7_domain_1(k5_numbers,0,1)) ),
    inference(let,[status(thm),assumptions([])],[i1_4_1_1_3_tmp__bintree2,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,redefinition_m2_finseq_1,dt_m1_finseq_2,dt_m2_finseq_1,cc1_finseq_1,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc11_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,commutativity_k7_domain_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,dt_k13_binarith,dt_k2_relat_1,dt_k5_numbers,dt_k7_domain_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d3_tarski,dh_c1_4_1_1_3__bintree2]),
    [interesting(0.5),file(bintree2,e5_4_1_1__bintree2),[file(bintree2,e5_4_1_1__bintree2)]]).

fof(e6_4_1_1__bintree2,plain,(
    m1_trees_4(k13_binarith(k5_numbers,1),k5_numbers,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc9_trees_2,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k7_domain_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_trees_4,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_m1_trees_4,dt_k13_binarith,dt_k2_relat_1,dt_k5_numbers,dt_k7_domain_1,dt_m1_finseq_1,dt_m1_trees_4,cc1_finseq_1,rc1_finseq_1,t3_subset,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e5_4_1_1__bintree2,d4_finseq_1]),
    [interesting(0.5),file(bintree2,e6_4_1_1__bintree2),[file(bintree2,e6_4_1_1__bintree2)]]).

fof(e9_4_1_1__bintree2,plain,(
    m1_trees_4(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)),k5_numbers,k7_domain_1(k5_numbers,0,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_c1_4__bintree2,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k7_domain_1,existence_m1_trees_4,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_4,redefinition_m2_finseq_1,dt_k13_binarith,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_trees_4,dt_m2_finseq_1,dt_c1_4_1__bintree2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_4_1_1__bintree2,e6_4_1_1__bintree2,t23_scmfsa_7]),
    [interesting(0.5),file(bintree2,e9_4_1_1__bintree2),[file(bintree2,e9_4_1_1__bintree2)]]).

fof(e10_4_1_1__bintree2,plain,(
    r2_hidden(k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1)),c1_4__bintree2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,cc3_trees_9,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m1_trees_4,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_4,redefinition_m2_finseq_1,dt_k13_binarith,dt_k13_finseq_1,dt_k3_finseq_2,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_trees_4,dt_m2_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,fc16_finseq_1,fc9_finseq_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_4_1_1__bintree2,e1_4__bintree2,d11_finseq_1]),
    [interesting(0.5),file(bintree2,e10_4_1_1__bintree2),[file(bintree2,e10_4_1_1__bintree2)]]).

fof(e13_4_1_1__bintree2,plain,(
    r2_hidden(c1_4_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4_1_1__bintree2,e11_4_1_1__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_trees_9,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_trees_2,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc2_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,dt_k13_binarith,dt_k5_numbers,dt_k8_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,dt_c1_4_1_1__bintree2,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_1_bintree2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e12_4_1_1__bintree2,e8_4_1_1__bintree2,e10_4_1_1__bintree2]),
    [interesting(0.5),file(bintree2,e13_4_1_1__bintree2),[file(bintree2,e13_4_1_1__bintree2)]]).

fof(i4_4_1_1__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i4_4_1_1__bintree2)]),
    [interesting(0.5),trivial,file(bintree2,i4_4_1_1__bintree2)]).

fof(i3_4_1_1__bintree2,plain,(
    r2_hidden(c1_4_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4_1_1__bintree2,e11_4_1_1__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[e13_4_1_1__bintree2,i4_4_1_1__bintree2]),
    [interesting(0.5),file(bintree2,i3_4_1_1__bintree2),[file(bintree2,i3_4_1_1__bintree2)]]).

fof(i2_4_1_1__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))))
      & ~ r2_hidden(c1_4_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4_1_1__bintree2,dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2]),discharge_asm(discharge,[e11_4_1_1__bintree2])],[e11_4_1_1__bintree2,i3_4_1_1__bintree2]),
    [interesting(0.5),file(bintree2,i2_4_1_1__bintree2),[file(bintree2,i2_4_1_1__bintree2)]]).

fof(i2_4_1_1_tmp__bintree2,plain,(
    ~ ( r2_hidden(c1_4_1_1__bintree2,k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))))
      & ~ r2_hidden(c1_4_1_1__bintree2,a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2]),discharge_asm(discharge,[dt_c1_4_1_1__bintree2])],[dt_c1_4_1_1__bintree2,i2_4_1_1__bintree2]),
    [interesting(0.5),i1_4_1_1__bintree2]).

fof(i1_4_1_1__bintree2,plain,(
    r1_tarski(k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))),a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2)) ),
    inference(let,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[i2_4_1_1_tmp__bintree2,rc3_trees_9,dt_m1_relset_1,cc3_trees_9,rc1_trees_2,rc2_finseq_1,rc9_trees_2,redefinition_m2_relset_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,commutativity_k7_domain_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,dt_k13_binarith,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,fc1_subset_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t2_tarski,fraenkel_a_2_1_bintree2,d3_tarski,dh_c1_4_1_1__bintree2]),
    [interesting(0.5),file(bintree2,i1_4_1_1__bintree2),[file(bintree2,i1_4_1_1__bintree2)]]).

fof(e2_4_1__bintree2,plain,(
    a_2_1_bintree2(c1_4__bintree2,c1_4_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[rc3_trees_9,dt_m1_relset_1,cc3_trees_9,rc1_trees_2,rc2_finseq_1,rc9_trees_2,redefinition_m2_relset_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,commutativity_k7_domain_1,reflexivity_r1_tarski,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,dt_k13_binarith,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,fc1_subset_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t2_tarski,fraenkel_a_2_1_bintree2,d10_xboole_0,e1_4_1_1__bintree2,i1_4_1_1__bintree2]),
    [interesting(0.65),file(bintree2,e2_4_1__bintree2),[file(bintree2,e2_4_1__bintree2)]]).

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(e3_4_1__bintree2,plain,(
    k1_trees_2(c1_4__bintree2,c1_4_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[existence_m1_relset_1,dt_m1_relset_1,fc4_trees_9,rc2_finseq_1,rc3_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_trees_2,rc1_finseq_1,rc1_margrel1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc7_finseq_1,rc8_finseq_1,commutativity_k2_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_tarski,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_nat_1,cc1_relset_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc14_finset_1,fc1_margrel1,fc1_ordinal2,fc2_finseq_1,fc2_finset_1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_trees_2,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k7_domain_1,existence_m1_trees_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k13_binarith,dt_k1_trees_2,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_4__bintree2,dt_c1_4_1__bintree2,cc1_finset_1,fc1_subset_1,fc4_subset_1,spc0_boole,spc1_boole,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_2_1_bintree2,fraenkel_a_2_1_trees_2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_4_1__bintree2,d5_trees_2]),
    [interesting(0.65),file(bintree2,e3_4_1__bintree2),[file(bintree2,e3_4_1__bintree2)]]).

fof(i3_4_1__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i3_4_1__bintree2)]),
    [interesting(0.65),trivial,file(bintree2,i3_4_1__bintree2)]).

fof(i2_4_1__bintree2,plain,(
    k1_trees_2(c1_4__bintree2,c1_4_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2])],[e3_4_1__bintree2,i3_4_1__bintree2]),
    [interesting(0.65),file(bintree2,i2_4_1__bintree2),[file(bintree2,i2_4_1__bintree2)]]).

fof(i1_4_1__bintree2,plain,
    ( ~ r2_hidden(c1_4_1__bintree2,k3_trees_1(c1_4__bintree2))
   => k1_trees_2(c1_4__bintree2,c1_4_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__bintree2,dt_c1_4_1__bintree2,e1_4__bintree2]),discharge_asm(discharge,[e1_4_1__bintree2])],[e1_4_1__bintree2,i2_4_1__bintree2]),
    [interesting(0.65),file(bintree2,i1_4_1__bintree2),[file(bintree2,i1_4_1__bintree2)]]).

fof(i1_4_1_tmp__bintree2,plain,
    ( m1_trees_1(c1_4_1__bintree2,c1_4__bintree2)
   => ( ~ r2_hidden(c1_4_1__bintree2,k3_trees_1(c1_4__bintree2))
     => k1_trees_2(c1_4__bintree2,c1_4_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_4_1__bintree2,k13_binarith(k5_numbers,1))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__bintree2,e1_4__bintree2]),discharge_asm(discharge,[dt_c1_4_1__bintree2])],[dt_c1_4_1__bintree2,i1_4_1__bintree2]),
    [interesting(0.8),e2_4__bintree2]).

fof(e2_4__bintree2,plain,(
    ! [A] : 
      ( m1_trees_1(A,c1_4__bintree2)
     => ( ~ r2_hidden(A,k3_trees_1(c1_4__bintree2))
       => k1_trees_2(c1_4__bintree2,A) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,A,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,A,k13_binarith(k5_numbers,1))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__bintree2,e1_4__bintree2])],[i1_4_1_tmp__bintree2,dh_c1_4_1__bintree2]),
    [interesting(0.8),file(bintree2,e2_4__bintree2),[file(bintree2,e2_4__bintree2)]]).

fof(d2_bintree1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( v1_bintree1(A)
      <=> ! [B] : 
            ( m1_trees_1(B,A)
           => ( ~ r2_hidden(B,k3_trees_1(A))
             => k1_trees_2(A,B) = k2_tarski(k7_finseq_1(B,k3_lang1(k1_numbers,0)),k7_finseq_1(B,k3_lang1(k1_numbers,1))) ) ) ) ) ),
    file(bintree1,d2_bintree1),
    [interesting(0.9),axiom,file(bintree1,d2_bintree1)]).

fof(e3_4__bintree2,plain,(
    v1_bintree1(c1_4__bintree2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__bintree2,e1_4__bintree2])],[existence_m1_relset_1,dt_m1_relset_1,rc2_finseq_1,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_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc16_finseq_1,fc4_trees_9,fc9_finseq_1,rc1_margrel1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_trees_9,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,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_k3_finseq_2,dt_k4_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,cc1_finseq_1,cc1_nat_1,cc1_relset_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,cc3_trees_9,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc1_ordinal2,fc1_trees_2,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_bintree1,rc1_finseq_1,rc1_finset_1,rc1_subset_1,rc1_trees_2,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k13_binarith,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k13_binarith,dt_k1_numbers,dt_k1_trees_2,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_lang1,dt_k3_trees_1,dt_k5_numbers,dt_k7_domain_1,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_4__bintree2,cc1_bintree1,cc1_finset_1,fc1_subset_1,fc2_finset_1,fc3_subset_1,fc4_subset_1,spc0_boole,spc1_boole,t1_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_4__bintree2,d2_bintree1]),
    [interesting(0.8),file(bintree2,e3_4__bintree2),[file(bintree2,e3_4__bintree2)]]).

fof(i3_4__bintree2,theorem,(
    $true ),
    introduced(tautology,[file(bintree2,i3_4__bintree2)]),
    [interesting(0.8),trivial,file(bintree2,i3_4__bintree2)]).

fof(i2_4__bintree2,plain,(
    v1_bintree1(c1_4__bintree2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__bintree2,e1_4__bintree2])],[e3_4__bintree2,i3_4__bintree2]),
    [interesting(0.8),file(bintree2,i2_4__bintree2),[file(bintree2,i2_4__bintree2)]]).

fof(i1_4__bintree2,plain,
    ( c1_4__bintree2 = k3_finseq_2(k7_domain_1(k5_numbers,0,1))
   => v1_bintree1(c1_4__bintree2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__bintree2]),discharge_asm(discharge,[e1_4__bintree2])],[e1_4__bintree2,i2_4__bintree2]),
    [interesting(0.8),file(bintree2,i1_4__bintree2),[file(bintree2,i1_4__bintree2)]]).

fof(i1_4_tmp__bintree2,plain,
    ( ( ~ v1_xboole_0(c1_4__bintree2)
      & v1_trees_1(c1_4__bintree2) )
   => ( c1_4__bintree2 = k3_finseq_2(k7_domain_1(k5_numbers,0,1))
     => v1_bintree1(c1_4__bintree2) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__bintree2])],[dt_c1_4__bintree2,i1_4__bintree2]),
    [interesting(1),t3_bintree2]).

fof(t3_bintree2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( A = k3_finseq_2(k7_domain_1(k5_numbers,0,1))
       => v1_bintree1(A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__bintree2,dh_c1_4__bintree2]),
    [interesting(1),file(bintree2,t3_bintree2),[file(bintree2,t3_bintree2)]]).