% Mizar ND problem: t5_bagorder,bagorder,142,62 
fof(dh_c1_7__bagorder,definition,
    ( ( m2_finseq_1(c1_7__bagorder,k5_numbers)
     => ( k9_wsierp_1(c1_7__bagorder) = 0
      <=> c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ) )
   => ! [A] : 
        ( m2_finseq_1(A,k5_numbers)
       => ( k9_wsierp_1(A) = 0
        <=> A = k4_finseqop(k5_numbers,k3_finseq_1(A),0) ) ) ),
    introduced(definition,[new_symbol(c1_7__bagorder),file(bagorder,c1_7__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_7__bagorder)]).

fof(e1_7_1__bagorder,assumption,(
    k9_wsierp_1(c1_7__bagorder) = 0 ),
    introduced(assumption,[file(bagorder,e1_7_1__bagorder)]),
    [interesting(0.65),axiom,file(bagorder,e1_7_1__bagorder)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

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

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

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

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

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

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(existence_m2_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(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(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_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k1_finseq_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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B)) ) ) ),
    file(finseq_2,k2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k2_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_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(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_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_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_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_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(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_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_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(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_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(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_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_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(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(fc1_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]).

fof(fc1_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_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc2_card_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_1,fc2_card_1),
    [interesting(0.9),axiom,file(card_1,fc2_card_1)]).

fof(fc4_polynom1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finset_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B))
        & v1_funcop_1(k2_finseq_2(A,B))
        & v1_matrlin(k2_finseq_2(A,B)) ) ) ),
    file(polynom1,fc4_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc4_polynom1)]).

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(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(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_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

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

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

fof(rc2_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(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(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

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

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

fof(existence_m2_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_k2_finseq_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(redefinition_k3_finseq_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(redefinition_k3_wsierp_1,definition,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k3_wsierp_1(A,B) = k1_funct_1(A,B) ) ),
    file(wsierp_1,k3_wsierp_1),
    [interesting(0.9),axiom,file(wsierp_1,k3_wsierp_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(redefinition_k4_finseqop,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => k4_finseqop(A,B,C) = k2_finseq_2(B,C) ) ),
    file(finseqop,k4_finseqop),
    [interesting(0.9),axiom,file(finseqop,k4_finseqop)]).

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

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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

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

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

fof(dt_k3_finseq_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_k3_wsierp_1,axiom,(
    ! [A,B] : 
      ( ( m1_finseq_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k3_wsierp_1(A,B),k1_numbers,k5_numbers) ) ),
    file(wsierp_1,k3_wsierp_1),
    [interesting(0.9),axiom,file(wsierp_1,k3_wsierp_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_k4_finseqop,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)) ) ),
    file(finseqop,k4_finseqop),
    [interesting(0.9),axiom,file(finseqop,k4_finseqop)]).

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_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(dt_c1_7__bagorder,assumption,(
    m2_finseq_1(c1_7__bagorder,k5_numbers) ),
    introduced(assumption,[file(bagorder,c1_7__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_7__bagorder)]).

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

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_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(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(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(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(dh_c1_7_1_1__bagorder,definition,
    ( ( m2_subset_1(c1_7_1_1__bagorder,k1_numbers,k5_numbers)
     => ( r2_hidden(c1_7_1_1__bagorder,k2_finseq_1(k3_finseq_1(c1_7__bagorder)))
       => k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),c1_7_1_1__bagorder) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r2_hidden(A,k2_finseq_1(k3_finseq_1(c1_7__bagorder)))
         => k3_wsierp_1(c1_7__bagorder,A) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),A) ) ) ),
    introduced(definition,[new_symbol(c1_7_1_1__bagorder),file(bagorder,c1_7_1_1__bagorder)]),
    [interesting(0.5),axiom,file(bagorder,c1_7_1_1__bagorder)]).

fof(e1_7_1_1__bagorder,assumption,(
    r2_hidden(c1_7_1_1__bagorder,k2_finseq_1(k3_finseq_1(c1_7__bagorder))) ),
    introduced(assumption,[file(bagorder,e1_7_1_1__bagorder)]),
    [interesting(0.5),axiom,file(bagorder,e1_7_1_1__bagorder)]).

fof(rc10_polynom1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc10_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc10_polynom1)]).

fof(rc13_polynom1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B)
      & v1_polynom1(B) ) ),
    file(polynom1,rc13_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc13_polynom1)]).

fof(rc8_polynom1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B) ) ),
    file(polynom1,rc8_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc8_polynom1)]).

fof(rc9_polynom1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc9_polynom1),
    [interesting(0.9),axiom,file(polynom1,rc9_polynom1)]).

fof(cc6_polynom1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => v1_polynom1(B) ) ) ),
    file(polynom1,cc6_polynom1),
    [interesting(0.9),axiom,file(polynom1,cc6_polynom1)]).

fof(fc4_ordinal2,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_ordinal2(k2_funcop_1(A,B)) ) ) ),
    file(ordinal2,fc4_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc4_ordinal2)]).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    [interesting(0.9),axiom,file(pboole,m1_pboole)]).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    [interesting(0.9),axiom,file(pboole,m1_pboole)]).

fof(redefinition_k2_pre_circ,definition,(
    ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ),
    file(pre_circ,k2_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,k2_pre_circ)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(dt_k2_pre_circ,axiom,(
    ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ),
    file(pre_circ,k2_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,k2_pre_circ)]).

fof(dt_c1_7_1_1__bagorder,assumption,(
    m2_subset_1(c1_7_1_1__bagorder,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(bagorder,c1_7_1_1__bagorder)]),
    [interesting(0.5),axiom,file(bagorder,c1_7_1_1__bagorder)]).

fof(e1_7_1_1_1__bagorder,assumption,(
    k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) != 0 ),
    introduced(assumption,[file(bagorder,e1_7_1_1_1__bagorder)]),
    [interesting(0.35),axiom,file(bagorder,e1_7_1_1_1__bagorder)]).

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(t5_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

fof(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

fof(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

fof(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(redefinition_k2_seq_1,definition,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seq_1,k2_seq_1),
    [interesting(0.9),axiom,file(seq_1,k2_seq_1)]).

fof(redefinition_k9_wsierp_1,definition,(
    ! [A] : 
      ( m1_finseq_1(A,k5_numbers)
     => k9_wsierp_1(A) = k15_rvsum_1(A) ) ),
    file(wsierp_1,k9_wsierp_1),
    [interesting(0.9),axiom,file(wsierp_1,k9_wsierp_1)]).

fof(dt_k15_rvsum_1,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k1_numbers)
     => m1_subset_1(k15_rvsum_1(A),k1_numbers) ) ),
    file(rvsum_1,k15_rvsum_1),
    [interesting(0.9),axiom,file(rvsum_1,k15_rvsum_1)]).

fof(dt_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ),
    file(seq_1,k2_seq_1),
    [interesting(0.9),axiom,file(seq_1,k2_seq_1)]).

fof(dt_k9_wsierp_1,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k5_numbers)
     => m2_subset_1(k9_wsierp_1(A),k1_numbers,k5_numbers) ) ),
    file(wsierp_1,k9_wsierp_1),
    [interesting(0.9),axiom,file(wsierp_1,k9_wsierp_1)]).

fof(de_c2_7__bagorder,definition,(
    c2_7__bagorder = c1_7__bagorder ),
    introduced(definition,[new_symbol(c2_7__bagorder),file(bagorder,c2_7__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_7__bagorder)]).

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

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

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

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(e1_7__bagorder,plain,(
    r1_tarski(k2_relat_1(c1_7__bagorder),k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[cc3_polynom1,rc11_polynom1,rc2_polynom1,rc3_relat_1,rc4_funct_1,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc4_subset_1,rc2_finseq_1,rc2_finset_1,rc2_ordinal1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,cc1_card_1,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_ordinal1,cc1_relat_1,cc1_xreal_0,cc2_card_5,cc2_finsub_1,cc2_funct_1,cc2_ordinal1,cc2_xreal_0,cc3_nat_1,cc3_ordinal1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc6_relat_1,fc8_relat_1,rc1_card_1,rc1_finset_1,rc1_nat_1,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_funct_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_nat_1,rc3_ordinal1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_card_5,cc1_nat_1,cc2_card_1,cc2_finset_1,cc2_nat_1,cc3_card_1,cc5_polynom1,fc11_finseq_1,fc1_finsub_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,rc1_card_5,rc3_polynom1,rc4_polynom1,reflexivity_r1_tarski,existence_m1_finseq_1,redefinition_k5_numbers,dt_k2_relat_1,dt_k5_numbers,dt_m1_finseq_1,dt_c1_7__bagorder,cc1_finseq_1,cc1_polynom1,rc1_finseq_1,rc1_funct_1,t3_subset,d4_finseq_1]),
    [interesting(0.8),file(bagorder,e1_7__bagorder),[file(bagorder,e1_7__bagorder)]]).

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

fof(e2_7__bagorder,plain,(
    r1_tarski(k2_relat_1(c1_7__bagorder),k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc11_polynom1,rc2_finseq_1,rc2_finset_1,rc2_ordinal1,rc2_polynom1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_polynom1,rc3_relat_1,rc3_xreal_0,rc4_finseq_1,rc4_funct_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc1_card_1,cc1_card_5,cc1_finseq_1,cc1_finsub_1,cc1_ordinal1,cc1_polynom1,cc1_xreal_0,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_funct_1,cc2_ordinal1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc7_xreal_0,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_funct_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc3_ordinal1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc2_card_1,cc2_nat_1,cc3_card_1,cc3_ordinal1,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc6_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k5_numbers,dt_k1_numbers,dt_k2_relat_1,dt_k5_numbers,dt_c1_7__bagorder,fc1_numbers,t3_subset,e1_7__bagorder,t1_xboole_1]),
    [interesting(0.8),file(bagorder,e2_7__bagorder),[file(bagorder,e2_7__bagorder)]]).

fof(e3_7__bagorder,plain,(
    m2_finseq_1(c1_7__bagorder,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[cc3_polynom1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc11_polynom1,rc2_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_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_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,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,t8_boole,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_relset_1,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,fc1_finsub_1,fc1_subset_1,fc6_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,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_k2_relat_1,dt_m1_finseq_1,dt_m2_finseq_1,dt_c1_7__bagorder,cc1_finseq_1,fc1_numbers,rc1_finseq_1,rc1_funct_1,t3_subset,e2_7__bagorder,d4_finseq_1]),
    [interesting(0.8),file(bagorder,e3_7__bagorder),[file(bagorder,e3_7__bagorder)]]).

fof(dt_c2_7__bagorder,plain,(
    m2_finseq_1(c2_7__bagorder,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__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,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_relat_1,rc4_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_polynom1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m1_subset_1,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_finseq_1,cc1_nat_1,cc1_ordinal1,cc1_relset_1,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_nat_1,cc2_ordinal1,cc3_card_1,cc5_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc1_finsub_1,fc1_ordinal2,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_funct_1,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,rc3_polynom1,rc4_finset_1,rc4_polynom1,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_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_polynom1,cc1_relat_1,cc3_ordinal1,t6_boole,t7_boole,t8_boole,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_m2_finseq_1,dt_c1_7__bagorder,fc1_numbers,de_c2_7__bagorder,e3_7__bagorder]),
    [interesting(0.8),file(bagorder,c2_7__bagorder),[file(bagorder,c2_7__bagorder)]]).

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

fof(e4_7_1_1_1__bagorder,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r2_hidden(A,k4_finseq_1(c1_7__bagorder))
       => r1_xreal_0(0,k3_wsierp_1(c1_7__bagorder,A)) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,fc5_polynom1,rc11_polynom1,rc2_finseq_1,rc2_polynom1,rc3_relat_1,rc4_funct_1,rc7_polynom1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc1_card_1,cc1_card_5,cc1_finsub_1,cc1_ordinal1,cc1_xreal_0,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc3_nat_1,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_1,rc1_card_5,rc1_finset_1,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_nat_1,rc2_ordinal1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc2_card_1,cc2_funct_1,cc2_nat_1,cc2_xreal_0,cc3_card_1,cc3_ordinal1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k3_wsierp_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_wsierp_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_7__bagorder,fc1_numbers,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,spc0_numerals,spc0_boole]),
    [interesting(0.35),file(bagorder,e4_7_1_1_1__bagorder),[file(bagorder,e4_7_1_1_1__bagorder)]]).

fof(e2_7_1_1_1__bagorder,plain,(
    ~ r1_xreal_0(k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder,dt_c1_7_1_1__bagorder,e1_7_1_1_1__bagorder])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finsub_1,cc1_relset_1,cc2_finsub_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,fc5_polynom1,rc11_polynom1,rc2_finseq_1,rc2_finset_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_finseq_1,rc4_funct_1,rc6_finseq_1,rc7_polynom1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc1_card_1,cc1_card_5,cc1_finseq_1,cc1_ordinal1,cc1_xreal_0,cc2_card_5,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_nat_1,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_polynom1,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_nat_1,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_funct_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_xreal_0,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k5_numbers,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc2_card_1,cc2_nat_1,cc2_xreal_0,cc3_card_1,cc3_ordinal1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_wsierp_1,dt_k3_wsierp_1,dt_c1_7__bagorder,dt_c1_7_1_1__bagorder,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e1_7_1_1_1__bagorder]),
    [interesting(0.35),file(bagorder,e2_7_1_1_1__bagorder),[file(bagorder,e2_7_1_1_1__bagorder)]]).

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(e2_7_1__bagorder,plain,(
    k2_finseq_1(k3_finseq_1(c1_7__bagorder)) = k4_finseq_1(c1_7__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc11_polynom1,rc2_finseq_1,rc2_polynom1,rc2_xreal_0,rc3_polynom1,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_polynom1,rc4_xreal_0,rc7_polynom1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc1_card_1,cc1_finsub_1,cc1_ordinal1,cc1_polynom1,cc2_card_5,cc2_finsub_1,cc2_ordinal1,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc14_polynom1,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,rc3_finseq_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc4_finseq_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_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,fc17_finseq_1,fc1_finseq_1,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc5_relat_1,fc7_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,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_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_7__bagorder,cc1_finseq_1,fc1_numbers,rc1_finseq_1,rc1_funct_1,d3_finseq_1]),
    [interesting(0.65),file(bagorder,e2_7_1__bagorder),[file(bagorder,e2_7_1__bagorder)]]).

fof(e3_7_1_1_1__bagorder,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & r2_hidden(A,k4_finseq_1(c2_7__bagorder))
      & ~ r1_xreal_0(k3_wsierp_1(c1_7__bagorder,A),0) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_1_1__bagorder,e1_7_1_1_1__bagorder,dt_c1_7__bagorder,e1_7_1_1__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,fc5_polynom1,rc11_polynom1,rc2_finseq_1,rc2_polynom1,rc3_relat_1,rc4_funct_1,rc7_polynom1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc1_card_1,cc1_card_5,cc1_finsub_1,cc1_ordinal1,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_1,rc1_card_5,rc1_finset_1,rc1_nat_1,rc1_ordinal1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_nat_1,rc2_ordinal1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc1_xreal_0,cc2_card_1,cc2_funct_1,cc2_nat_1,cc2_xreal_0,cc3_card_1,cc3_nat_1,cc3_ordinal1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_finseq_1,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k3_wsierp_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_finseq_1,dt_k3_finseq_1,dt_k3_wsierp_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_7__bagorder,dt_c1_7_1_1__bagorder,dt_c2_7__bagorder,de_c2_7__bagorder,fc1_numbers,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,spc0_numerals,spc0_boole,e2_7_1_1_1__bagorder,e2_7_1__bagorder,e1_7_1_1__bagorder]),
    [interesting(0.35),file(bagorder,e3_7_1_1_1__bagorder),[file(bagorder,e3_7_1_1_1__bagorder)]]).

fof(t115_rvsum_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k1_numbers)
     => ~ ( ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( r2_hidden(B,k4_finseq_1(A))
               => r1_xreal_0(0,k2_seq_1(k5_numbers,k1_numbers,A,B)) ) )
          & ? [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
              & r2_hidden(B,k4_finseq_1(A))
              & ~ r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),0) )
          & r1_xreal_0(k15_rvsum_1(A),0) ) ) ),
    file(rvsum_1,t115_rvsum_1),
    [interesting(0.9),axiom,file(rvsum_1,t115_rvsum_1)]).

fof(e5_7_1_1_1__bagorder,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7_1_1__bagorder,e1_7_1_1_1__bagorder,dt_c1_7__bagorder,e1_7_1_1__bagorder])],[cc3_polynom1,fc5_polynom1,rc11_polynom1,rc2_polynom1,rc3_relat_1,rc4_funct_1,rc7_polynom1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_card_1,cc1_card_5,cc1_finsub_1,cc1_ordinal1,cc1_relset_1,cc1_xreal_0,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc3_nat_1,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc4_subset_1,rc1_card_1,rc1_card_5,rc1_finset_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_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc2_card_1,cc2_funct_1,cc2_nat_1,cc2_xreal_0,cc3_card_1,cc3_ordinal1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc5_relat_1,fc7_relat_1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k3_wsierp_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k9_wsierp_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k15_rvsum_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_wsierp_1,dt_k4_finseq_1,dt_k5_numbers,dt_k9_wsierp_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_7__bagorder,dt_c2_7__bagorder,de_c2_7__bagorder,fc1_numbers,t1_subset,t7_boole,spc0_numerals,spc0_boole,e4_7_1_1_1__bagorder,e1_7_1__bagorder,e3_7_1_1_1__bagorder,t115_rvsum_1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.35),file(bagorder,e5_7_1_1_1__bagorder),[file(bagorder,e5_7_1_1_1__bagorder)]]).

fof(i2_7_1_1_1__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i2_7_1_1_1__bagorder)]),
    [interesting(0.35),trivial,file(bagorder,i2_7_1_1_1__bagorder)]).

fof(i1_7_1_1_1__bagorder,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7_1_1__bagorder,e1_7_1_1_1__bagorder,dt_c1_7__bagorder,e1_7_1_1__bagorder])],[e5_7_1_1_1__bagorder,i2_7_1_1_1__bagorder]),
    [interesting(0.35),file(bagorder,i1_7_1_1_1__bagorder),[file(bagorder,i1_7_1_1_1__bagorder)]]).

fof(e2_7_1_1__bagorder,plain,(
    k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) = 0 ),
    inference(discharge_asm,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7_1_1__bagorder,dt_c1_7__bagorder,e1_7_1_1__bagorder]),discharge_asm(discharge,[e1_7_1_1_1__bagorder])],[e1_7_1_1_1__bagorder,i1_7_1_1_1__bagorder]),
    [interesting(0.5),file(bagorder,e2_7_1_1__bagorder),[file(bagorder,e2_7_1_1__bagorder)]]).

fof(d2_finseq_2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B) ) ),
    file(finseq_2,d2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,d2_finseq_2)]).

fof(e3_7_1__bagorder,plain,(
    k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) = k2_pre_circ(k2_finseq_1(k3_finseq_1(c1_7__bagorder)),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,rc10_polynom1,rc11_polynom1,rc13_polynom1,rc2_finseq_1,rc3_polynom1,rc3_relat_1,rc4_funct_1,rc4_polynom1,rc7_polynom1,rc8_polynom1,rc9_polynom1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_card_1,cc1_card_5,cc1_finsub_1,cc1_ordinal1,cc1_polynom1,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc5_polynom1,cc6_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_ordinal2,fc4_relat_1,rc1_card_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_card_1,rc2_card_5,rc2_finset_1,rc2_nat_1,rc2_ordinal1,rc2_polynom1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc4_finseq_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_pboole,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_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_pboole,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_relat_1,cc2_card_1,cc2_funct_1,cc2_nat_1,cc2_xreal_0,cc3_card_1,cc3_ordinal1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_finseq_1,fc1_finsub_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc4_polynom1,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k2_finseq_1,redefinition_k2_pre_circ,redefinition_k3_finseq_1,redefinition_k4_finseqop,redefinition_k5_numbers,dt_k2_finseq_1,dt_k2_finseq_2,dt_k2_funcop_1,dt_k2_pre_circ,dt_k3_finseq_1,dt_k4_finseqop,dt_k5_numbers,dt_c1_7__bagorder,cc1_xreal_0,cc3_nat_1,spc0_numerals,spc0_boole,d2_finseq_2]),
    [interesting(0.65),file(bagorder,e3_7_1__bagorder),[file(bagorder,e3_7_1__bagorder)]]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t13_funcop_1)]).

fof(e3_7_1_1__bagorder,plain,(
    k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),c1_7_1_1__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7_1_1__bagorder,dt_c1_7__bagorder,e1_7_1_1__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,rc10_polynom1,rc11_polynom1,rc13_polynom1,rc2_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_polynom1,rc9_polynom1,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_card_1,cc1_card_5,cc1_finsub_1,cc1_ordinal1,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_ordinal2,fc4_relat_1,fc5_polynom1,rc1_card_1,rc1_card_5,rc1_finset_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_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_pboole,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_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_pboole,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc1_xreal_0,cc2_card_1,cc2_funct_1,cc2_nat_1,cc3_card_1,cc3_nat_1,cc3_ordinal1,fc1_finseq_1,fc1_finsub_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc4_polynom1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k2_pre_circ,redefinition_k3_finseq_1,redefinition_k3_wsierp_1,redefinition_k4_finseqop,redefinition_k5_numbers,dt_k1_funct_1,dt_k2_finseq_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k3_finseq_1,dt_k3_wsierp_1,dt_k4_finseqop,dt_k5_numbers,dt_c1_7__bagorder,dt_c1_7_1_1__bagorder,t1_subset,t7_boole,spc0_numerals,spc0_boole,e2_7_1_1__bagorder,e3_7_1__bagorder,e1_7_1_1__bagorder,t13_funcop_1]),
    [interesting(0.5),file(bagorder,e3_7_1_1__bagorder),[file(bagorder,e3_7_1_1__bagorder)]]).

fof(i3_7_1_1__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i3_7_1_1__bagorder)]),
    [interesting(0.5),trivial,file(bagorder,i3_7_1_1__bagorder)]).

fof(i2_7_1_1__bagorder,plain,(
    k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),c1_7_1_1__bagorder) ),
    inference(conclusion,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7_1_1__bagorder,dt_c1_7__bagorder,e1_7_1_1__bagorder])],[e3_7_1_1__bagorder,i3_7_1_1__bagorder]),
    [interesting(0.5),file(bagorder,i2_7_1_1__bagorder),[file(bagorder,i2_7_1_1__bagorder)]]).

fof(i1_7_1_1__bagorder,plain,
    ( r2_hidden(c1_7_1_1__bagorder,k2_finseq_1(k3_finseq_1(c1_7__bagorder)))
   => k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),c1_7_1_1__bagorder) ),
    inference(discharge_asm,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7_1_1__bagorder,dt_c1_7__bagorder]),discharge_asm(discharge,[e1_7_1_1__bagorder])],[e1_7_1_1__bagorder,i2_7_1_1__bagorder]),
    [interesting(0.5),file(bagorder,i1_7_1_1__bagorder),[file(bagorder,i1_7_1_1__bagorder)]]).

fof(i1_7_1_1_tmp__bagorder,plain,
    ( m2_subset_1(c1_7_1_1__bagorder,k1_numbers,k5_numbers)
   => ( r2_hidden(c1_7_1_1__bagorder,k2_finseq_1(k3_finseq_1(c1_7__bagorder)))
     => k3_wsierp_1(c1_7__bagorder,c1_7_1_1__bagorder) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),c1_7_1_1__bagorder) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7__bagorder]),discharge_asm(discharge,[dt_c1_7_1_1__bagorder])],[dt_c1_7_1_1__bagorder,i1_7_1_1__bagorder]),
    [interesting(0.65),e5_7_1__bagorder]).

fof(e5_7_1__bagorder,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r2_hidden(A,k2_finseq_1(k3_finseq_1(c1_7__bagorder)))
       => k3_wsierp_1(c1_7__bagorder,A) = k3_wsierp_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0),A) ) ) ),
    inference(let,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7__bagorder])],[i1_7_1_1_tmp__bagorder,dh_c1_7_1_1__bagorder]),
    [interesting(0.65),file(bagorder,e5_7_1__bagorder),[file(bagorder,e5_7_1__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(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t19_funcop_1)]).

fof(e4_7_1__bagorder,plain,(
    k2_finseq_1(k3_finseq_1(c1_7__bagorder)) = k4_finseq_1(k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,rc10_polynom1,rc11_polynom1,rc13_polynom1,rc2_finseq_1,rc3_polynom1,rc3_relat_1,rc4_funct_1,rc4_polynom1,rc7_polynom1,rc8_polynom1,rc9_polynom1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_card_1,cc1_finsub_1,cc1_ordinal1,cc1_polynom1,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,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_ordinal2,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_finseq_1,rc4_xreal_0,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_pboole,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_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_pboole,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_card_5,cc1_finseq_1,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,cc6_polynom1,fc11_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_finsub_1,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc4_polynom1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_card_5,rc1_finseq_1,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,rc8_finseq_1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k2_finseq_1,redefinition_k2_pre_circ,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_finseqop,redefinition_k5_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_relat_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_finseqop,dt_k5_numbers,dt_c1_7__bagorder,fc1_finset_1,fc2_subset_1,t3_subset,spc0_numerals,spc0_boole,e3_7_1__bagorder,t19_funcop_1]),
    [interesting(0.65),file(bagorder,e4_7_1__bagorder),[file(bagorder,e4_7_1__bagorder)]]).

fof(t17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k4_finseq_1(A) = k4_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t17_finseq_1)]).

fof(e6_7_1__bagorder,plain,(
    c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ),
    inference(mizar_by,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,rc11_polynom1,rc2_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,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_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,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,fc5_polynom1,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_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,dt_k1_card_1,dt_k1_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,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,fc17_finseq_1,fc1_finseq_1,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc2_card_1,fc4_polynom1,fc5_relat_1,fc7_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,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k3_wsierp_1,redefinition_k4_finseq_1,redefinition_k4_finseqop,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_finseq_1,dt_k3_finseq_1,dt_k3_wsierp_1,dt_k4_finseq_1,dt_k4_finseqop,dt_k5_numbers,dt_m2_subset_1,dt_c1_7__bagorder,cc1_finseq_1,fc1_numbers,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,spc0_numerals,spc0_boole,e5_7_1__bagorder,e2_7_1__bagorder,e4_7_1__bagorder,t17_finseq_1]),
    [interesting(0.65),file(bagorder,e6_7_1__bagorder),[file(bagorder,e6_7_1__bagorder)]]).

fof(i2_7_1__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i2_7_1__bagorder)]),
    [interesting(0.65),trivial,file(bagorder,i2_7_1__bagorder)]).

fof(i1_7_1__bagorder,plain,(
    c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ),
    inference(conclusion,[status(thm),assumptions([e1_7_1__bagorder,dt_c1_7__bagorder])],[e6_7_1__bagorder,i2_7_1__bagorder]),
    [interesting(0.65),file(bagorder,i1_7_1__bagorder),[file(bagorder,i1_7_1__bagorder)]]).

fof(e4_7__bagorder,plain,
    ( k9_wsierp_1(c1_7__bagorder) = 0
   => c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bagorder]),discharge_asm(discharge,[e1_7_1__bagorder])],[e1_7_1__bagorder,i1_7_1__bagorder]),
    [interesting(0.8),file(bagorder,e4_7__bagorder),[file(bagorder,e4_7__bagorder)]]).

fof(e5_7__bagorder,assumption,(
    c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ),
    introduced(assumption,[file(bagorder,e5_7__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e5_7__bagorder)]).

fof(t111_rvsum_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k15_rvsum_1(k4_finseqop(k1_numbers,A,0)) = 0 ) ),
    file(rvsum_1,t111_rvsum_1),
    [interesting(0.9),axiom,file(rvsum_1,t111_rvsum_1)]).

fof(e6_7__bagorder,plain,(
    k9_wsierp_1(c1_7__bagorder) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__bagorder,e5_7__bagorder])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_polynom1,fc14_finset_1,fc4_subset_1,rc11_polynom1,rc2_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,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_card_1,cc1_card_5,cc1_finsub_1,cc1_ordinal1,cc1_xreal_0,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_ordinal1,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_card_1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_1,rc1_card_5,rc1_finset_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_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_polynom1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,dt_k1_card_1,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_nat_1,cc1_polynom1,cc1_relat_1,cc2_card_1,cc2_funct_1,cc2_nat_1,cc3_card_1,cc3_ordinal1,fc1_finsub_1,fc1_ordinal2,fc1_subset_1,fc4_polynom1,rc1_finseq_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseqop,redefinition_k5_numbers,redefinition_k9_wsierp_1,redefinition_m2_subset_1,dt_k15_rvsum_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseqop,dt_k5_numbers,dt_k9_wsierp_1,dt_m2_subset_1,dt_c1_7__bagorder,fc1_numbers,spc0_numerals,spc0_boole,e5_7__bagorder,t111_rvsum_1]),
    [interesting(0.8),file(bagorder,e6_7__bagorder),[file(bagorder,e6_7__bagorder)]]).

fof(i4_7__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i4_7__bagorder)]),
    [interesting(0.8),trivial,file(bagorder,i4_7__bagorder)]).

fof(i3_7__bagorder,plain,(
    k9_wsierp_1(c1_7__bagorder) = 0 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__bagorder,e5_7__bagorder])],[e6_7__bagorder,i4_7__bagorder]),
    [interesting(0.8),file(bagorder,i3_7__bagorder),[file(bagorder,i3_7__bagorder)]]).

fof(i2_7__bagorder,plain,
    ( c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0)
   => k9_wsierp_1(c1_7__bagorder) = 0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__bagorder]),discharge_asm(discharge,[e5_7__bagorder])],[e5_7__bagorder,i3_7__bagorder]),
    [interesting(0.8),file(bagorder,i2_7__bagorder),[file(bagorder,i2_7__bagorder)]]).

fof(i1_7__bagorder,plain,
    ( k9_wsierp_1(c1_7__bagorder) = 0
  <=> c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__bagorder])],[e4_7__bagorder,i2_7__bagorder]),
    [interesting(0.8),file(bagorder,i1_7__bagorder),[file(bagorder,i1_7__bagorder)]]).

fof(i1_7_tmp__bagorder,plain,
    ( m2_finseq_1(c1_7__bagorder,k5_numbers)
   => ( k9_wsierp_1(c1_7__bagorder) = 0
    <=> c1_7__bagorder = k4_finseqop(k5_numbers,k3_finseq_1(c1_7__bagorder),0) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__bagorder])],[dt_c1_7__bagorder,i1_7__bagorder]),
    [interesting(1),t5_bagorder]).

fof(t5_bagorder,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ( k9_wsierp_1(A) = 0
      <=> A = k4_finseqop(k5_numbers,k3_finseq_1(A),0) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__bagorder,dh_c1_7__bagorder]),
    [interesting(1),file(bagorder,t5_bagorder),[file(bagorder,t5_bagorder)]]).