% Mizar ND problem: t1_bagorder,bagorder,43,70 
fof(dh_c1_1__bagorder,definition,
    ( ! [A,B] : 
        ( ( r2_hidden(B,c1_1__bagorder)
          & r2_hidden(B,A) )
       => ( k4_xboole_0(c1_1__bagorder,k1_tarski(B)) = k4_xboole_0(A,k1_tarski(B))
        <=> c1_1__bagorder = A ) )
   => ! [C,D,E] : 
        ( ( r2_hidden(E,C)
          & r2_hidden(E,D) )
       => ( k4_xboole_0(C,k1_tarski(E)) = k4_xboole_0(D,k1_tarski(E))
        <=> C = D ) ) ),
    introduced(definition,[new_symbol(c1_1__bagorder),file(bagorder,c1_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_1__bagorder)]).

fof(dh_c2_1__bagorder,definition,
    ( ! [A] : 
        ( ( r2_hidden(A,c1_1__bagorder)
          & r2_hidden(A,c2_1__bagorder) )
       => ( k4_xboole_0(c1_1__bagorder,k1_tarski(A)) = k4_xboole_0(c2_1__bagorder,k1_tarski(A))
        <=> c1_1__bagorder = c2_1__bagorder ) )
   => ! [B,C] : 
        ( ( r2_hidden(C,c1_1__bagorder)
          & r2_hidden(C,B) )
       => ( k4_xboole_0(c1_1__bagorder,k1_tarski(C)) = k4_xboole_0(B,k1_tarski(C))
        <=> c1_1__bagorder = B ) ) ),
    introduced(definition,[new_symbol(c2_1__bagorder),file(bagorder,c2_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_1__bagorder)]).

fof(dh_c3_1__bagorder,definition,
    ( ( ( r2_hidden(c3_1__bagorder,c1_1__bagorder)
        & r2_hidden(c3_1__bagorder,c2_1__bagorder) )
     => ( k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder))
      <=> c1_1__bagorder = c2_1__bagorder ) )
   => ! [A] : 
        ( ( r2_hidden(A,c1_1__bagorder)
          & r2_hidden(A,c2_1__bagorder) )
       => ( k4_xboole_0(c1_1__bagorder,k1_tarski(A)) = k4_xboole_0(c2_1__bagorder,k1_tarski(A))
        <=> c1_1__bagorder = c2_1__bagorder ) ) ),
    introduced(definition,[new_symbol(c3_1__bagorder),file(bagorder,c3_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c3_1__bagorder)]).

fof(e1_1__bagorder,assumption,
    ( r2_hidden(c3_1__bagorder,c1_1__bagorder)
    & r2_hidden(c3_1__bagorder,c2_1__bagorder) ),
    introduced(assumption,[file(bagorder,e1_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e1_1__bagorder)]).

fof(e1_1_1__bagorder,assumption,(
    k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)) ),
    introduced(assumption,[file(bagorder,e1_1_1__bagorder)]),
    [interesting(0.65),axiom,file(bagorder,e1_1_1__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(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(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(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(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(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_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(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_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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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_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_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(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(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(fc2_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc2_relat_1)]).

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(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_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_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(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(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(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(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_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(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(fc9_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc9_finset_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(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(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(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_c1_1__bagorder,assumption,(
    $true ),
    introduced(assumption,[file(bagorder,c1_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_1__bagorder)]).

fof(dt_c2_1__bagorder,assumption,(
    $true ),
    introduced(assumption,[file(bagorder,c2_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_1__bagorder)]).

fof(dt_c3_1__bagorder,assumption,(
    $true ),
    introduced(assumption,[file(bagorder,c3_1__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c3_1__bagorder)]).

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(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(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t46_zfmisc_1)]).

fof(e1_1_1_1__bagorder,plain,(
    c1_1__bagorder = k2_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,e1_1__bagorder])],[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,dt_k1_xboole_0,cc1_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc2_relat_1,fc3_polynom1,fc4_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc9_finset_1,rc1_card_5,rc1_finset_1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_xboole_0,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e1_1__bagorder,t46_zfmisc_1]),
    [interesting(0.5),file(bagorder,e1_1_1_1__bagorder),[file(bagorder,e1_1_1_1__bagorder)]]).

fof(fc3_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc3_relat_1)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

fof(fc12_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc12_finset_1)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(t39_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t39_xboole_1)]).

fof(e2_1_1_1__bagorder,plain,(
    k2_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k2_xboole_0(k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)),k1_tarski(c3_1__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,e1_1_1__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_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc2_relat_1,fc3_polynom1,fc3_relat_1,fc4_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_boole,t1_subset,t3_boole,t4_boole,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc12_finset_1,fc9_finset_1,rc1_card_5,rc1_finset_1,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k2_xboole_0,dt_k4_xboole_0,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,fc1_finset_1,fc2_subset_1,e1_1_1__bagorder,t39_xboole_1]),
    [interesting(0.5),file(bagorder,e2_1_1_1__bagorder),[file(bagorder,e2_1_1_1__bagorder)]]).

fof(e3_1_1_1__bagorder,plain,(
    k2_xboole_0(k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)),k1_tarski(c3_1__bagorder)) = k2_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_1__bagorder,dt_c3_1__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_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc2_relat_1,fc3_polynom1,fc3_relat_1,fc4_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_boole,t1_subset,t3_boole,t4_boole,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc12_finset_1,fc9_finset_1,rc1_card_5,rc1_finset_1,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k2_xboole_0,dt_k4_xboole_0,dt_c2_1__bagorder,dt_c3_1__bagorder,fc1_finset_1,fc2_subset_1,t39_xboole_1]),
    [interesting(0.5),file(bagorder,e3_1_1_1__bagorder),[file(bagorder,e3_1_1_1__bagorder)]]).

fof(e4_1_1_1__bagorder,plain,(
    k2_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)) = c2_1__bagorder ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,e1_1__bagorder])],[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,dt_k1_xboole_0,cc1_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc2_relat_1,fc3_polynom1,fc4_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc9_finset_1,rc1_card_5,rc1_finset_1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_xboole_0,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e1_1__bagorder,t46_zfmisc_1]),
    [interesting(0.5),file(bagorder,e4_1_1_1__bagorder),[file(bagorder,e4_1_1_1__bagorder)]]).

fof(e2_1_1__bagorder,plain,(
    c1_1__bagorder = c2_1__bagorder ),
    inference(iterative_eq,[status(thm),assumptions([e1_1_1__bagorder,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,e1_1__bagorder])],[e1_1_1_1__bagorder,e2_1_1_1__bagorder,e3_1_1_1__bagorder,e4_1_1_1__bagorder]),
    [interesting(0.65),file(bagorder,e2_1_1__bagorder),[file(bagorder,e2_1_1__bagorder)]]).

fof(i2_1_1__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i2_1_1__bagorder)]),
    [interesting(0.65),trivial,file(bagorder,i2_1_1__bagorder)]).

fof(i1_1_1__bagorder,plain,(
    c1_1__bagorder = c2_1__bagorder ),
    inference(conclusion,[status(thm),assumptions([e1_1_1__bagorder,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,e1_1__bagorder])],[e2_1_1__bagorder,i2_1_1__bagorder]),
    [interesting(0.65),file(bagorder,i1_1_1__bagorder),[file(bagorder,i1_1_1__bagorder)]]).

fof(e2_1__bagorder,plain,
    ( k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder))
   => c1_1__bagorder = c2_1__bagorder ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,e1_1__bagorder]),discharge_asm(discharge,[e1_1_1__bagorder])],[e1_1_1__bagorder,i1_1_1__bagorder]),
    [interesting(0.8),file(bagorder,e2_1__bagorder),[file(bagorder,e2_1__bagorder)]]).

fof(e3_1__bagorder,plain,
    ( c1_1__bagorder = c2_1__bagorder
   => k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__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_ordinal1,cc2_funct_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_polynom1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc3_relat_1,fc4_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,rc7_finseq_1,t1_subset,t3_boole,t4_boole,cc1_card_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc3_ordinal1,fc12_finset_1,rc1_card_5,rc1_finset_1,t6_boole,t7_boole,t8_boole,dt_k1_tarski,dt_k4_xboole_0,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,fc1_finset_1,fc2_subset_1]),
    [interesting(0.8),file(bagorder,e3_1__bagorder),[file(bagorder,e3_1__bagorder)]]).

fof(i4_1__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i4_1__bagorder)]),
    [interesting(0.8),trivial,file(bagorder,i4_1__bagorder)]).

fof(i3_1__bagorder,plain,
    ( c1_1__bagorder = c2_1__bagorder
   => k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder])],[e3_1__bagorder,i4_1__bagorder]),
    [interesting(0.8),file(bagorder,i3_1__bagorder),[file(bagorder,i3_1__bagorder)]]).

fof(i2_1__bagorder,plain,
    ( k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder))
  <=> c1_1__bagorder = c2_1__bagorder ),
    inference(conclusion,[status(thm),assumptions([e1_1__bagorder,dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder])],[e2_1__bagorder,i3_1__bagorder]),
    [interesting(0.8),file(bagorder,i2_1__bagorder),[file(bagorder,i2_1__bagorder)]]).

fof(i1_1__bagorder,plain,
    ( ( r2_hidden(c3_1__bagorder,c1_1__bagorder)
      & r2_hidden(c3_1__bagorder,c2_1__bagorder) )
   => ( k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder))
    <=> c1_1__bagorder = c2_1__bagorder ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder]),discharge_asm(discharge,[e1_1__bagorder])],[e1_1__bagorder,i2_1__bagorder]),
    [interesting(0.8),file(bagorder,i1_1__bagorder),[file(bagorder,i1_1__bagorder)]]).

fof(i1_1_tmp__bagorder,plain,
    ( ( r2_hidden(c3_1__bagorder,c1_1__bagorder)
      & r2_hidden(c3_1__bagorder,c2_1__bagorder) )
   => ( k4_xboole_0(c1_1__bagorder,k1_tarski(c3_1__bagorder)) = k4_xboole_0(c2_1__bagorder,k1_tarski(c3_1__bagorder))
    <=> c1_1__bagorder = c2_1__bagorder ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder])],[dt_c1_1__bagorder,dt_c2_1__bagorder,dt_c3_1__bagorder,i1_1__bagorder]),
    [interesting(1),t1_bagorder]).

fof(t1_bagorder,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(C,A)
        & r2_hidden(C,B) )
     => ( k4_xboole_0(A,k1_tarski(C)) = k4_xboole_0(B,k1_tarski(C))
      <=> A = B ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__bagorder,dh_c1_1__bagorder,dh_c2_1__bagorder,dh_c3_1__bagorder]),
    [interesting(1),file(bagorder,t1_bagorder),[file(bagorder,t1_bagorder)]]).