% Mizar ND problem: t3_bagorder,bagorder,112,68 
fof(dh_c1_5__bagorder,definition,
    ( ( ( v1_relat_1(c1_5__bagorder)
        & v1_funct_1(c1_5__bagorder) )
     => ! [A] : 
          ( r2_hidden(A,k1_relat_1(c1_5__bagorder))
         => k5_relat_1(k9_finseq_1(A),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,A)) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( r2_hidden(C,k1_relat_1(B))
           => k5_relat_1(k9_finseq_1(C),B) = k9_finseq_1(k1_funct_1(B,C)) ) ) ),
    introduced(definition,[new_symbol(c1_5__bagorder),file(bagorder,c1_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_5__bagorder)]).

fof(dh_c2_5__bagorder,definition,
    ( ( r2_hidden(c2_5__bagorder,k1_relat_1(c1_5__bagorder))
     => k5_relat_1(k9_finseq_1(c2_5__bagorder),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,c2_5__bagorder)) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(c1_5__bagorder))
       => k5_relat_1(k9_finseq_1(A),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,A)) ) ),
    introduced(definition,[new_symbol(c2_5__bagorder),file(bagorder,c2_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_5__bagorder)]).

fof(e1_5__bagorder,assumption,(
    r2_hidden(c2_5__bagorder,k1_relat_1(c1_5__bagorder)) ),
    introduced(assumption,[file(bagorder,e1_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e1_5__bagorder)]).

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

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

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

fof(rc11_polynom1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_seq_1(A)
      & v7_seqm_3(A)
      & v1_polynom1(A) ) ),
    file(polynom1,rc11_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc11_polynom1)]).

fof(rc12_polynom1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,k5_numbers)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funct_2(B,A,k5_numbers)
      & v1_seq_1(B)
      & v7_seqm_3(B)
      & v1_polynom1(B) ) ),
    file(polynom1,rc12_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc12_polynom1)]).

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

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

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

fof(rc7_polynom1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A)
      & v7_seqm_3(A) ) ),
    file(polynom1,rc7_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc7_polynom1)]).

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

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc1_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    [interesting(0.9),axiom,file(card_1,cc1_card_1)]).

fof(cc1_finsub_1,theorem,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,cc1_finsub_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_card_5,theorem,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(card_5,cc2_card_5),
    [interesting(0.9),axiom,file(card_5,cc2_card_5)]).

fof(cc2_finsub_1,theorem,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,cc2_finsub_1)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(cc3_polynom1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_seqm_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) ) ) ),
    file(polynom1,cc3_polynom1),
    [interesting(0.9),axiom,file(polynom1,cc3_polynom1)]).

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

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

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

fof(fc1_numbers,theorem,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    [interesting(0.9),axiom,file(numbers,fc1_numbers)]).

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

fof(fc5_polynom1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_matrlin(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B))
        & v1_finset_1(k1_funct_1(A,B))
        & v1_finseq_1(k1_funct_1(A,B)) ) ) ),
    file(polynom1,fc5_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc5_polynom1)]).

fof(rc1_card_1,theorem,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    [interesting(0.9),axiom,file(card_1,rc1_card_1)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_card_1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    [interesting(0.9),axiom,file(card_1,rc2_card_1)]).

fof(rc2_card_5,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_5,rc2_card_5),
    [interesting(0.9),axiom,file(card_5,rc2_card_5)]).

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_polynom1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_funcop_1(A)
      & v1_matrlin(A) ) ),
    file(polynom1,rc2_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc2_polynom1)]).

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_polynom1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_card_3(A) ) ),
    file(polynom1,rc3_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc3_polynom1)]).

fof(rc4_polynom1,theorem,(
    ? [A] : 
      ( m1_finseq_1(A,k5_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_card_3(A) ) ),
    file(polynom1,rc4_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc4_polynom1)]).

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

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

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

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

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

fof(cc1_card_5,theorem,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(card_5,cc1_card_5),
    [interesting(0.9),axiom,file(card_5,cc1_card_5)]).

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_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

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_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(cc1_polynom1,theorem,(
    ! [A] : 
      ( m1_finseq_1(A,k5_numbers)
     => v1_card_3(A) ) ),
    file(polynom1,cc1_polynom1),
    [interesting(0.9),axiom,file(polynom1,cc1_polynom1)]).

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

fof(cc2_card_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)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    [interesting(0.9),axiom,file(card_1,cc2_card_1)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(cc2_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

fof(cc3_card_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_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    [interesting(0.9),axiom,file(card_1,cc3_card_1)]).

fof(cc4_polynom1,theorem,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k5_numbers)
     => ( ( v1_funct_1(B)
          & v1_funct_2(B,A,k5_numbers) )
       => ( v1_funct_1(B)
          & v1_funct_2(B,A,k5_numbers)
          & v7_seqm_3(B) ) ) ) ),
    file(polynom1,cc4_polynom1),
    [interesting(0.9),axiom,file(polynom1,cc4_polynom1)]).

fof(cc5_polynom1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_polynom1(A) ) ) ),
    file(polynom1,cc5_polynom1),
    [interesting(0.9),axiom,file(polynom1,cc5_polynom1)]).

fof(fc11_polynom1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & ~ v1_xboole_0(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v1_funcop_1(k5_finseq_1(A))
        & v1_matrlin(k5_finseq_1(A)) ) ) ),
    file(polynom1,fc11_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc11_polynom1)]).

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_finsub_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,fc1_finsub_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(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_card_5,theorem,(
    ? [A] : ~ v1_finset_1(A) ),
    file(card_5,rc1_card_5),
    [interesting(0.9),axiom,file(card_5,rc1_card_5)]).

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_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

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

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

fof(rc2_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

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

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

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

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

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

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

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

fof(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_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_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]).

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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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_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_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

fof(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

fof(fc10_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc10_relat_1)]).

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(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_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(fc9_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc9_relat_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(redefinition_k5_finseqop,definition,(
    ! [A,B,C,D] : 
      ( ( m1_finseq_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => k5_finseqop(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(finseqop,k5_finseqop),
    [interesting(0.9),axiom,file(finseqop,k5_finseqop)]).

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_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k5_finseqop,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_finseq_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => m2_finseq_1(k5_finseqop(A,B,C,D),B) ) ),
    file(finseqop,k5_finseqop),
    [interesting(0.9),axiom,file(finseqop,k5_finseqop)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_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(dt_c1_5__bagorder,assumption,
    ( v1_relat_1(c1_5__bagorder)
    & v1_funct_1(c1_5__bagorder) ),
    introduced(assumption,[file(bagorder,c1_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_5__bagorder)]).

fof(dt_c2_5__bagorder,assumption,(
    $true ),
    introduced(assumption,[file(bagorder,c2_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_5__bagorder)]).

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(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

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

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc14_polynom1,theorem,
    ( 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_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0) ),
    file(polynom1,fc14_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc14_polynom1)]).

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(fc20_polynom1,theorem,
    ( 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_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0)
    & v1_polynom1(k1_xboole_0) ),
    file(polynom1,fc20_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc20_polynom1)]).

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(fc2_ordinal1,theorem,
    ( 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_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(fc3_polynom1,theorem,
    ( 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_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_matrlin(k1_xboole_0) ),
    file(polynom1,fc3_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc3_polynom1)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

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

fof(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(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_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(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

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

fof(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(de_c3_5__bagorder,definition,(
    c3_5__bagorder = k1_relat_1(c1_5__bagorder) ),
    introduced(definition,[new_symbol(c3_5__bagorder),file(bagorder,c3_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c3_5__bagorder)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_5__bagorder,plain,(
    r2_hidden(k1_funct_1(c1_5__bagorder,c2_5__bagorder),k2_relat_1(c1_5__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc1_finseq_1,cc3_polynom1,fc5_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,dt_k1_xboole_0,cc1_card_5,cc1_ordinal1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc3_ordinal1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_5__bagorder,dt_c2_5__bagorder,rc1_funct_1,t1_subset,t7_boole,e1_5__bagorder,d5_funct_1]),
    [interesting(0.8),file(bagorder,e2_5__bagorder),[file(bagorder,e2_5__bagorder)]]).

fof(e3_5__bagorder,plain,
    ( ~ v1_xboole_0(k1_relat_1(c1_5__bagorder))
    & ~ v1_xboole_0(k2_relat_1(c1_5__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc1_finseq_1,cc3_polynom1,fc5_polynom1,rc11_polynom1,rc1_finseq_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_polynom1,rc8_finseq_1,existence_m1_subset_1,dt_k1_xboole_0,dt_m1_subset_1,cc1_card_5,cc1_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc5_relat_1,fc6_relat_1,rc1_card_5,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_5__bagorder,dt_c2_5__bagorder,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc7_relat_1,fc8_relat_1,t1_subset,t6_boole,t7_boole,e2_5__bagorder,e1_5__bagorder]),
    [interesting(0.8),file(bagorder,e3_5__bagorder),[file(bagorder,e3_5__bagorder)]]).

fof(dt_c3_5__bagorder,plain,(
    ~ v1_xboole_0(c3_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_polynom1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc5_relat_1,fc6_relat_1,rc1_card_5,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_subset,dt_k1_relat_1,dt_k2_relat_1,dt_c1_5__bagorder,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc7_relat_1,fc8_relat_1,t6_boole,t7_boole,t8_boole,de_c3_5__bagorder,e3_5__bagorder]),
    [interesting(0.8),file(bagorder,c3_5__bagorder),[file(bagorder,c3_5__bagorder)]]).

fof(de_c4_5__bagorder,definition,(
    c4_5__bagorder = k2_relat_1(c1_5__bagorder) ),
    introduced(definition,[new_symbol(c4_5__bagorder),file(bagorder,c4_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c4_5__bagorder)]).

fof(dt_c4_5__bagorder,plain,(
    ~ v1_xboole_0(c4_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_polynom1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc5_relat_1,fc6_relat_1,rc1_card_5,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_subset,dt_k1_relat_1,dt_k2_relat_1,dt_c1_5__bagorder,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc7_relat_1,fc8_relat_1,t6_boole,t7_boole,t8_boole,de_c4_5__bagorder,e3_5__bagorder]),
    [interesting(0.8),file(bagorder,c4_5__bagorder),[file(bagorder,c4_5__bagorder)]]).

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

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_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(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(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(de_c5_5__bagorder,definition,(
    c5_5__bagorder = c1_5__bagorder ),
    introduced(definition,[new_symbol(c5_5__bagorder),file(bagorder,c5_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c5_5__bagorder)]).

fof(redefinition_k4_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.9),axiom,file(funct_2,d1_funct_2)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.9),axiom,file(relset_1,t11_relset_1)]).

fof(e4_5__bagorder,plain,
    ( v1_funct_1(c1_5__bagorder)
    & v1_funct_2(c1_5__bagorder,c3_5__bagorder,c4_5__bagorder)
    & m2_relset_1(c1_5__bagorder,c3_5__bagorder,c4_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[antisymmetry_r2_hidden,cc1_finsub_1,cc1_funct_2,cc2_finsub_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_card_5,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relat_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,cc3_polynom1,cc5_funct_2,cc5_polynom1,cc6_funct_2,fc11_finseq_1,fc14_finset_1,fc17_finseq_1,fc1_finsub_1,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc11_polynom1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_2,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_ordinal1,rc2_polynom1,rc2_relat_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc3_relat_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_relset_1,dt_m2_relset_1,dt_c1_5__bagorder,dt_c3_5__bagorder,dt_c4_5__bagorder,de_c3_5__bagorder,de_c4_5__bagorder,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_funct_1,t3_subset,t6_boole,d1_funct_2,t11_relset_1]),
    [interesting(0.8),file(bagorder,e4_5__bagorder),[file(bagorder,e4_5__bagorder)]]).

fof(dt_c5_5__bagorder,plain,
    ( v1_funct_1(c5_5__bagorder)
    & v1_funct_2(c5_5__bagorder,c3_5__bagorder,c4_5__bagorder)
    & m2_relset_1(c5_5__bagorder,c3_5__bagorder,c4_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_finsub_1,cc1_funct_2,cc1_ordinal1,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc3_ordinal1,cc5_funct_2,cc6_funct_2,fc1_finsub_1,fc1_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_c1_5__bagorder,dt_c3_5__bagorder,dt_c4_5__bagorder,de_c3_5__bagorder,de_c4_5__bagorder,de_c5_5__bagorder,e4_5__bagorder]),
    [interesting(0.8),file(bagorder,c5_5__bagorder),[file(bagorder,c5_5__bagorder)]]).

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

fof(existence_m2_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(de_c6_5__bagorder,definition,(
    c6_5__bagorder = k9_finseq_1(c2_5__bagorder) ),
    introduced(definition,[new_symbol(c6_5__bagorder),file(bagorder,c6_5__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c6_5__bagorder)]).

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

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(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_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

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

fof(dt_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(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(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_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(dt_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(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(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

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(e5_5__bagorder,plain,(
    k2_relat_1(k9_finseq_1(c2_5__bagorder)) = k1_tarski(c2_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__bagorder])],[cc3_polynom1,rc11_polynom1,rc3_relat_1,rc4_funct_1,rc7_polynom1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc1_card_1,cc1_finsub_1,cc1_ordinal1,cc2_card_5,cc2_finsub_1,cc2_ordinal1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_polynom1,fc1_ordinal2,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_1,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_nat_1,rc2_ordinal1,rc2_polynom1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc1_xreal_0,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_nat_1,cc3_card_1,cc3_nat_1,cc3_ordinal1,cc5_polynom1,fc11_finseq_1,fc11_polynom1,fc12_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_finsub_1,fc1_numbers,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_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,redefinition_k2_finseq_1,redefinition_k4_finseq_1,redefinition_k9_finseq_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_relat_1,dt_k4_finseq_1,dt_k9_finseq_1,dt_c2_5__bagorder,cc1_finseq_1,fc1_finset_1,fc2_subset_1,rc1_finseq_1,rc1_funct_1,spc1_numerals,spc1_boole,t55_finseq_1]),
    [interesting(0.8),file(bagorder,e5_5__bagorder),[file(bagorder,e5_5__bagorder)]]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t37_zfmisc_1)]).

fof(e6_5__bagorder,plain,(
    r1_tarski(k2_relat_1(k9_finseq_1(c2_5__bagorder)),c3_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc3_polynom1,rc11_polynom1,rc2_polynom1,rc3_relat_1,rc4_funct_1,rc7_polynom1,dt_k1_xboole_0,cc1_finseq_1,cc1_finsub_1,cc1_ordinal1,cc2_finsub_1,cc2_ordinal1,fc11_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_finseq_1,rc1_ordinal1,rc2_ordinal1,rc3_finseq_1,rc3_funct_1,rc3_ordinal1,rc6_finseq_1,rc8_finseq_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_m1_subset_1,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_finset_1,cc2_funct_1,cc3_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_finseq_1,fc17_finseq_1,fc1_finsub_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_card_5,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k9_finseq_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k9_finseq_1,dt_c1_5__bagorder,dt_c2_5__bagorder,dt_c3_5__bagorder,de_c3_5__bagorder,fc1_finset_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e5_5__bagorder,e1_5__bagorder,t37_zfmisc_1]),
    [interesting(0.8),file(bagorder,e6_5__bagorder),[file(bagorder,e6_5__bagorder)]]).

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

fof(e7_5__bagorder,plain,(
    m2_finseq_1(k9_finseq_1(c2_5__bagorder),c3_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc3_polynom1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc11_polynom1,rc2_xreal_0,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc1_card_1,cc1_finsub_1,cc1_ordinal1,cc1_relset_1,cc1_xreal_0,cc2_card_5,cc2_finsub_1,cc2_ordinal1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc1_numbers,fc1_ordinal2,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc4_subset_1,rc1_card_1,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc4_finseq_1,rc4_polynom1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_relset_1,dt_c1_5__bagorder,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_nat_1,cc3_card_1,cc3_ordinal1,cc5_polynom1,fc11_finseq_1,fc11_polynom1,fc12_finseq_1,fc17_finseq_1,fc1_finsub_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_1,redefinition_k9_finseq_1,redefinition_m2_finseq_1,dt_k2_relat_1,dt_k9_finseq_1,dt_m1_finseq_1,dt_m2_finseq_1,dt_c2_5__bagorder,dt_c3_5__bagorder,de_c3_5__bagorder,cc1_finseq_1,rc1_finseq_1,rc1_funct_1,t3_subset,e6_5__bagorder,d4_finseq_1]),
    [interesting(0.8),file(bagorder,e7_5__bagorder),[file(bagorder,e7_5__bagorder)]]).

fof(dt_c6_5__bagorder,plain,(
    m2_finseq_1(c6_5__bagorder,c3_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_card_1,cc1_finsub_1,cc1_xreal_0,cc2_card_5,cc2_finsub_1,cc2_xreal_0,cc3_nat_1,cc3_polynom1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc11_polynom1,rc1_card_1,rc1_nat_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc3_nat_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m1_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc1_card_5,cc1_nat_1,cc1_ordinal1,cc1_relset_1,cc2_card_1,cc2_finset_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc5_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc1_finsub_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc4_subset_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc2_finseq_1,rc2_nat_1,rc2_ordinal1,rc2_polynom1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc3_polynom1,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_relat_1,dt_k5_finseq_1,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,dt_c1_5__bagorder,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_polynom1,cc1_relat_1,cc2_funct_1,cc3_ordinal1,fc11_polynom1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,existence_m2_finseq_1,redefinition_k9_finseq_1,redefinition_m2_finseq_1,dt_k9_finseq_1,dt_m2_finseq_1,dt_c2_5__bagorder,dt_c3_5__bagorder,de_c3_5__bagorder,de_c6_5__bagorder,e7_5__bagorder]),
    [interesting(0.8),file(bagorder,c6_5__bagorder),[file(bagorder,c6_5__bagorder)]]).

fof(e1_5_1__bagorder,plain,(
    k5_relat_1(k9_finseq_1(c2_5__bagorder),c1_5__bagorder) = k5_finseqop(c3_5__bagorder,c4_5__bagorder,c6_5__bagorder,c5_5__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_numbers,dt_k5_ordinal2,cc1_card_1,cc1_finsub_1,cc1_xreal_0,cc2_card_5,cc2_finsub_1,cc2_xreal_0,cc3_nat_1,cc3_polynom1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_numbers,fc1_ordinal2,rc11_polynom1,rc12_polynom1,rc1_card_1,rc1_nat_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_nat_1,rc2_polynom1,rc3_nat_1,rc3_polynom1,rc3_relat_1,rc4_funct_1,rc4_polynom1,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc1_card_5,cc1_finseq_1,cc1_funct_2,cc1_nat_1,cc1_ordinal1,cc1_polynom1,cc1_relset_1,cc2_card_1,cc2_finset_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc4_polynom1,cc5_polynom1,fc11_finseq_1,fc11_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc1_finsub_1,fc1_subset_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc4_subset_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc2_finseq_1,rc2_ordinal1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc3_ordinal1,cc5_funct_2,cc6_funct_2,fc10_relat_1,fc12_finseq_1,fc1_funct_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc2_funct_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,redefinition_k5_finseqop,redefinition_k9_finseq_1,dt_k5_finseqop,dt_k5_relat_1,dt_k9_finseq_1,dt_c1_5__bagorder,dt_c2_5__bagorder,dt_c3_5__bagorder,dt_c4_5__bagorder,dt_c5_5__bagorder,dt_c6_5__bagorder,de_c3_5__bagorder,de_c4_5__bagorder,de_c5_5__bagorder,de_c6_5__bagorder]),
    [interesting(0.65),file(bagorder,e1_5_1__bagorder),[file(bagorder,e1_5_1__bagorder)]]).

fof(redefinition_k1_partfun1,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(partfun1,k1_partfun1),
    [interesting(0.9),axiom,file(partfun1,k1_partfun1)]).

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ),
    file(partfun1,k1_partfun1),
    [interesting(0.9),axiom,file(partfun1,k1_partfun1)]).

fof(t39_finseq_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ! [D] : 
              ( m2_finseq_1(D,B)
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( D = k9_finseq_1(A)
                   => k1_partfun1(k5_numbers,B,B,C,D,E) = k9_finseq_1(k1_funct_1(E,A)) ) ) ) ) ) ),
    file(finseq_2,t39_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,t39_finseq_2)]).

fof(e2_5_1__bagorder,plain,(
    k5_finseqop(c3_5__bagorder,c4_5__bagorder,c6_5__bagorder,c5_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,c2_5__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_card_1,cc1_finsub_1,cc1_funct_2,cc1_xreal_0,cc2_card_5,cc2_finsub_1,cc2_xreal_0,cc3_nat_1,cc3_polynom1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc5_polynom1,rc11_polynom1,rc12_polynom1,rc1_card_1,rc1_nat_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_polynom1,rc3_relat_1,rc4_finseq_1,rc4_funct_1,rc4_polynom1,rc6_finseq_1,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k5_finseq_1,dt_k5_ordinal2,dt_k5_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,cc1_card_5,cc1_finseq_1,cc1_nat_1,cc1_ordinal1,cc1_polynom1,cc1_relset_1,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc4_polynom1,cc5_funct_2,cc5_polynom1,cc6_funct_2,fc10_relat_1,fc11_finseq_1,fc11_polynom1,fc12_finseq_1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc1_finsub_1,fc1_funct_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_finseq_1,fc3_polynom1,fc4_finseq_1,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc2_finseq_1,rc2_funct_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_finseq_1,existence_m2_relset_1,redefinition_k1_partfun1,redefinition_k5_finseqop,redefinition_k5_numbers,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_partfun1,dt_k5_finseqop,dt_k5_numbers,dt_k9_finseq_1,dt_m2_finseq_1,dt_m2_relset_1,dt_c1_5__bagorder,dt_c2_5__bagorder,dt_c3_5__bagorder,dt_c4_5__bagorder,dt_c5_5__bagorder,dt_c6_5__bagorder,de_c3_5__bagorder,de_c4_5__bagorder,de_c5_5__bagorder,de_c6_5__bagorder,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,t6_boole,t7_boole,t8_boole,t39_finseq_2]),
    [interesting(0.65),file(bagorder,e2_5_1__bagorder),[file(bagorder,e2_5_1__bagorder)]]).

fof(e8_5__bagorder,plain,(
    k5_relat_1(k9_finseq_1(c2_5__bagorder),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,c2_5__bagorder)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc11_polynom1,rc12_polynom1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc7_polynom1,dt_k1_numbers,dt_k5_ordinal2,cc1_card_1,cc1_finsub_1,cc1_xreal_0,cc2_card_5,cc2_finsub_1,cc2_xreal_0,cc3_nat_1,cc3_polynom1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_numbers,fc1_ordinal2,fc5_polynom1,rc1_card_1,rc1_nat_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_nat_1,rc2_polynom1,rc3_nat_1,rc3_polynom1,rc4_polynom1,redefinition_k5_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc1_card_5,cc1_finseq_1,cc1_funct_2,cc1_nat_1,cc1_ordinal1,cc1_polynom1,cc1_relset_1,cc2_card_1,cc2_finset_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc4_polynom1,cc5_polynom1,fc11_polynom1,fc14_finset_1,fc1_finsub_1,fc1_subset_1,fc4_subset_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc2_finseq_1,rc2_ordinal1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k5_finseq_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc3_ordinal1,cc5_funct_2,cc6_funct_2,fc10_relat_1,fc12_finseq_1,fc1_funct_1,fc3_finseq_1,fc4_finseq_1,fc9_relat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc2_funct_1,rc2_relat_1,redefinition_k5_finseqop,redefinition_k9_finseq_1,dt_k1_funct_1,dt_k5_finseqop,dt_k5_relat_1,dt_k9_finseq_1,dt_c1_5__bagorder,dt_c2_5__bagorder,dt_c3_5__bagorder,dt_c4_5__bagorder,dt_c5_5__bagorder,dt_c6_5__bagorder,e1_5_1__bagorder,e2_5_1__bagorder]),
    [interesting(0.8),file(bagorder,e8_5__bagorder),[file(bagorder,e8_5__bagorder)]]).

fof(i4_5__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i4_5__bagorder)]),
    [interesting(0.8),trivial,file(bagorder,i4_5__bagorder)]).

fof(i3_5__bagorder,plain,(
    k5_relat_1(k9_finseq_1(c2_5__bagorder),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,c2_5__bagorder)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder,e1_5__bagorder])],[e8_5__bagorder,i4_5__bagorder]),
    [interesting(0.8),file(bagorder,i3_5__bagorder),[file(bagorder,i3_5__bagorder)]]).

fof(i2_5__bagorder,plain,
    ( r2_hidden(c2_5__bagorder,k1_relat_1(c1_5__bagorder))
   => k5_relat_1(k9_finseq_1(c2_5__bagorder),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,c2_5__bagorder)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bagorder,dt_c2_5__bagorder]),discharge_asm(discharge,[e1_5__bagorder])],[e1_5__bagorder,i3_5__bagorder]),
    [interesting(0.8),file(bagorder,i2_5__bagorder),[file(bagorder,i2_5__bagorder)]]).

fof(i2_5_tmp__bagorder,plain,
    ( r2_hidden(c2_5__bagorder,k1_relat_1(c1_5__bagorder))
   => k5_relat_1(k9_finseq_1(c2_5__bagorder),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,c2_5__bagorder)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bagorder]),discharge_asm(discharge,[dt_c2_5__bagorder])],[dt_c2_5__bagorder,i2_5__bagorder]),
    [interesting(0.8),i1_5__bagorder]).

fof(i1_5__bagorder,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(c1_5__bagorder))
     => k5_relat_1(k9_finseq_1(A),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__bagorder])],[i2_5_tmp__bagorder,dh_c2_5__bagorder]),
    [interesting(0.8),file(bagorder,i1_5__bagorder),[file(bagorder,i1_5__bagorder)]]).

fof(i1_5_tmp__bagorder,plain,
    ( ( v1_relat_1(c1_5__bagorder)
      & v1_funct_1(c1_5__bagorder) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(c1_5__bagorder))
       => k5_relat_1(k9_finseq_1(A),c1_5__bagorder) = k9_finseq_1(k1_funct_1(c1_5__bagorder,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__bagorder])],[dt_c1_5__bagorder,i1_5__bagorder]),
    [interesting(1),t3_bagorder]).

fof(t3_bagorder,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k5_relat_1(k9_finseq_1(B),A) = k9_finseq_1(k1_funct_1(A,B)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__bagorder,dh_c1_5__bagorder]),
    [interesting(1),file(bagorder,t3_bagorder),[file(bagorder,t3_bagorder)]]).