% Mizar ND problem: t4_bagorder,bagorder,128,15 
fof(dh_c1_6__bagorder,definition,
    ( ( ( v1_relat_1(c1_6__bagorder)
        & v1_funct_1(c1_6__bagorder) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(A)
                  & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(B))
                  & r1_tarski(k2_relat_1(A),k1_relat_1(B))
                  & r1_rfinseq(c1_6__bagorder,A) )
               => r1_rfinseq(k5_relat_1(c1_6__bagorder,B),k5_relat_1(A,B)) ) ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D) )
           => ! [E] : 
                ( ( v1_relat_1(E)
                  & v1_funct_1(E) )
               => ( ( k1_relat_1(C) = k1_relat_1(D)
                    & r1_tarski(k2_relat_1(C),k1_relat_1(E))
                    & r1_tarski(k2_relat_1(D),k1_relat_1(E))
                    & r1_rfinseq(C,D) )
                 => r1_rfinseq(k5_relat_1(C,E),k5_relat_1(D,E)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__bagorder),file(bagorder,c1_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_6__bagorder)]).

fof(dh_c2_6__bagorder,definition,
    ( ( ( v1_relat_1(c2_6__bagorder)
        & v1_funct_1(c2_6__bagorder) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(c2_6__bagorder)
              & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(A))
              & r1_tarski(k2_relat_1(c2_6__bagorder),k1_relat_1(A))
              & r1_rfinseq(c1_6__bagorder,c2_6__bagorder) )
           => r1_rfinseq(k5_relat_1(c1_6__bagorder,A),k5_relat_1(c2_6__bagorder,A)) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(B)
                & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(C))
                & r1_tarski(k2_relat_1(B),k1_relat_1(C))
                & r1_rfinseq(c1_6__bagorder,B) )
             => r1_rfinseq(k5_relat_1(c1_6__bagorder,C),k5_relat_1(B,C)) ) ) ) ),
    introduced(definition,[new_symbol(c2_6__bagorder),file(bagorder,c2_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_6__bagorder)]).

fof(dh_c3_6__bagorder,definition,
    ( ( ( v1_relat_1(c3_6__bagorder)
        & v1_funct_1(c3_6__bagorder) )
     => ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(c2_6__bagorder)
          & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(c3_6__bagorder))
          & r1_tarski(k2_relat_1(c2_6__bagorder),k1_relat_1(c3_6__bagorder))
          & r1_rfinseq(c1_6__bagorder,c2_6__bagorder) )
       => r1_rfinseq(k5_relat_1(c1_6__bagorder,c3_6__bagorder),k5_relat_1(c2_6__bagorder,c3_6__bagorder)) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(c2_6__bagorder)
            & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(A))
            & r1_tarski(k2_relat_1(c2_6__bagorder),k1_relat_1(A))
            & r1_rfinseq(c1_6__bagorder,c2_6__bagorder) )
         => r1_rfinseq(k5_relat_1(c1_6__bagorder,A),k5_relat_1(c2_6__bagorder,A)) ) ) ),
    introduced(definition,[new_symbol(c3_6__bagorder),file(bagorder,c3_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c3_6__bagorder)]).

fof(e1_6__bagorder,assumption,(
    k1_relat_1(c1_6__bagorder) = k1_relat_1(c2_6__bagorder) ),
    introduced(assumption,[file(bagorder,e1_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e1_6__bagorder)]).

fof(e2_6__bagorder,assumption,(
    r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(c3_6__bagorder)) ),
    introduced(assumption,[file(bagorder,e2_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e2_6__bagorder)]).

fof(e3_6__bagorder,assumption,(
    r1_tarski(k2_relat_1(c2_6__bagorder),k1_relat_1(c3_6__bagorder)) ),
    introduced(assumption,[file(bagorder,e3_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e3_6__bagorder)]).

fof(e4_6__bagorder,assumption,(
    r1_rfinseq(c1_6__bagorder,c2_6__bagorder) ),
    introduced(assumption,[file(bagorder,e4_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,e4_6__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_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_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(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(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

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

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

fof(cc1_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_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_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_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(fc14_polynom1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0) ),
    file(polynom1,fc14_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc14_polynom1)]).

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

fof(fc20_polynom1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0)
    & v1_polynom1(k1_xboole_0) ),
    file(polynom1,fc20_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc20_polynom1)]).

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

fof(fc2_ordinal1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(fc3_polynom1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_matrlin(k1_xboole_0) ),
    file(polynom1,fc3_polynom1),
    [interesting(0.9),axiom,file(polynom1,fc3_polynom1)]).

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

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

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

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

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

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

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

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_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_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

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

fof(cc2_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_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc3_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc3_funct_2)]).

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

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

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

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

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

fof(rc1_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_funct_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc2_funct_2)]).

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

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

fof(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(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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc2_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc2_funct_2)]).

fof(fc1_finsub_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,fc1_finsub_1)]).

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

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

fof(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(symmetry_r1_rfinseq,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => ( r1_rfinseq(A,B)
       => r1_rfinseq(B,A) ) ) ),
    file(rfinseq,r1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]).

fof(reflexivity_r1_rfinseq,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => r1_rfinseq(A,A) ) ),
    file(rfinseq,r1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]).

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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(dt_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(dt_c1_6__bagorder,assumption,
    ( v1_relat_1(c1_6__bagorder)
    & v1_funct_1(c1_6__bagorder) ),
    introduced(assumption,[file(bagorder,c1_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c1_6__bagorder)]).

fof(dt_c2_6__bagorder,assumption,
    ( v1_relat_1(c2_6__bagorder)
    & v1_funct_1(c2_6__bagorder) ),
    introduced(assumption,[file(bagorder,c2_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c2_6__bagorder)]).

fof(dt_c3_6__bagorder,assumption,
    ( v1_relat_1(c3_6__bagorder)
    & v1_funct_1(c3_6__bagorder) ),
    introduced(assumption,[file(bagorder,c3_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c3_6__bagorder)]).

fof(dh_c4_6__bagorder,definition,
    ( ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
        & v3_funct_2(A,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
        & m2_relset_1(A,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
        & c1_6__bagorder = k5_relat_1(A,c2_6__bagorder) )
   => ( v1_funct_1(c4_6__bagorder)
      & v1_funct_2(c4_6__bagorder,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
      & v3_funct_2(c4_6__bagorder,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
      & m2_relset_1(c4_6__bagorder,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
      & c1_6__bagorder = k5_relat_1(c4_6__bagorder,c2_6__bagorder) ) ),
    introduced(definition,[new_symbol(c4_6__bagorder),file(bagorder,c4_6__bagorder)]),
    [interesting(0.8),axiom,file(bagorder,c4_6__bagorder)]).

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

fof(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(t6_rfinseq,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k1_relat_1(A) = k1_relat_1(B)
           => ( r1_rfinseq(A,B)
            <=> ? [C] : 
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k1_relat_1(A),k1_relat_1(A))
                  & v3_funct_2(C,k1_relat_1(A),k1_relat_1(A))
                  & m2_relset_1(C,k1_relat_1(A),k1_relat_1(A))
                  & A = k5_relat_1(C,B) ) ) ) ) ) ),
    file(rfinseq,t6_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,t6_rfinseq)]).

fof(e5_6__bagorder,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
      & v3_funct_2(A,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
      & m2_relset_1(A,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
      & c1_6__bagorder = k5_relat_1(A,c2_6__bagorder) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bagorder,dt_c2_6__bagorder,e1_6__bagorder,e4_6__bagorder])],[cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_funct_2,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_relat_1,cc2_finsub_1,cc2_funct_1,cc3_funct_2,cc3_ordinal1,cc5_funct_2,cc6_funct_2,fc10_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_funct_2,rc2_relat_1,rc2_subset_1,rc3_funct_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc2_funct_2,fc1_finsub_1,fc1_subset_1,rc1_funct_2,t3_subset,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k5_relat_1,dt_m2_relset_1,dt_c1_6__bagorder,dt_c2_6__bagorder,fc1_funct_1,rc1_funct_1,e1_6__bagorder,e4_6__bagorder,t6_rfinseq]),
    [interesting(0.8),file(bagorder,e5_6__bagorder),[file(bagorder,e5_6__bagorder)]]).

fof(dt_c4_6__bagorder,plain,
    ( v1_funct_1(c4_6__bagorder)
    & v1_funct_2(c4_6__bagorder,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
    & v3_funct_2(c4_6__bagorder,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder))
    & m2_relset_1(c4_6__bagorder,k1_relat_1(c1_6__bagorder),k1_relat_1(c1_6__bagorder)) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bagorder,dt_c2_6__bagorder,e1_6__bagorder,e4_6__bagorder])],[dh_c4_6__bagorder,e5_6__bagorder]),
    [interesting(0.8),file(bagorder,c4_6__bagorder),[file(bagorder,c4_6__bagorder)]]).

fof(e6_6__bagorder,plain,(
    c1_6__bagorder = k5_relat_1(c4_6__bagorder,c2_6__bagorder) ),
    inference(consider,[status(thm),assumptions([dt_c1_6__bagorder,dt_c2_6__bagorder,e1_6__bagorder,e4_6__bagorder])],[dh_c4_6__bagorder,e5_6__bagorder]),
    [interesting(0.8),file(bagorder,e6_6__bagorder),[file(bagorder,e6_6__bagorder)]]).

fof(t55_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_1),
    [interesting(0.9),axiom,file(relat_1,t55_relat_1)]).

fof(e9_6__bagorder,plain,(
    k5_relat_1(c1_6__bagorder,c3_6__bagorder) = k5_relat_1(c4_6__bagorder,k5_relat_1(c2_6__bagorder,c3_6__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_6__bagorder,dt_c1_6__bagorder,dt_c2_6__bagorder,e1_6__bagorder,e4_6__bagorder])],[cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_funct_2,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_relat_1,cc2_finsub_1,cc2_funct_1,cc3_funct_2,cc3_ordinal1,cc5_funct_2,cc6_funct_2,fc10_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_funct_2,rc2_relat_1,rc2_subset_1,rc3_funct_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc2_funct_2,fc1_finsub_1,fc1_subset_1,rc1_funct_2,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_m2_relset_1,fc1_funct_1,rc1_funct_1,dt_k5_relat_1,dt_c1_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder,dt_c4_6__bagorder,e6_6__bagorder,t55_relat_1]),
    [interesting(0.8),file(bagorder,e9_6__bagorder),[file(bagorder,e9_6__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(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.9),axiom,file(relat_1,t46_relat_1)]).

fof(e7_6__bagorder,plain,(
    k1_relat_1(k5_relat_1(c1_6__bagorder,c3_6__bagorder)) = k1_relat_1(c1_6__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__bagorder,dt_c3_6__bagorder,e2_6__bagorder])],[cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_relat_1,cc2_finsub_1,cc2_funct_1,cc3_ordinal1,fc10_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_finsub_1,fc1_funct_1,fc1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k2_relat_1,dt_k5_relat_1,dt_c1_6__bagorder,dt_c3_6__bagorder,t3_subset,e2_6__bagorder,t46_relat_1]),
    [interesting(0.8),file(bagorder,e7_6__bagorder),[file(bagorder,e7_6__bagorder)]]).

fof(e8_6__bagorder,plain,(
    k1_relat_1(k5_relat_1(c2_6__bagorder,c3_6__bagorder)) = k1_relat_1(c2_6__bagorder) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__bagorder,dt_c3_6__bagorder,e3_6__bagorder])],[cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc5_polynom1,fc11_finseq_1,fc12_relat_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_relat_1,cc2_finsub_1,cc2_funct_1,cc3_ordinal1,fc10_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_finsub_1,fc1_funct_1,fc1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k2_relat_1,dt_k5_relat_1,dt_c2_6__bagorder,dt_c3_6__bagorder,t3_subset,e3_6__bagorder,t46_relat_1]),
    [interesting(0.8),file(bagorder,e8_6__bagorder),[file(bagorder,e8_6__bagorder)]]).

fof(e10_6__bagorder,plain,(
    r1_rfinseq(k5_relat_1(c1_6__bagorder,c3_6__bagorder),k5_relat_1(c2_6__bagorder,c3_6__bagorder)) ),
    inference(mizar_by,[status(thm),assumptions([e4_6__bagorder,e1_6__bagorder,dt_c1_6__bagorder,e2_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder,e3_6__bagorder])],[cc1_finseq_1,cc3_polynom1,rc11_polynom1,rc1_finseq_1,rc2_polynom1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc7_polynom1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_5,cc1_funct_2,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc5_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc20_polynom1,fc2_finseq_1,fc2_ordinal1,fc3_polynom1,fc4_relat_1,rc1_card_5,rc1_finset_1,rc1_ordinal1,rc2_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_relat_1,cc2_finsub_1,cc2_funct_1,cc3_funct_2,cc3_ordinal1,cc5_funct_2,cc6_funct_2,fc10_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_funct_2,rc2_relat_1,rc2_subset_1,rc3_funct_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,cc2_funct_2,fc1_finsub_1,fc1_subset_1,rc1_funct_2,t3_subset,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k5_relat_1,dt_m2_relset_1,dt_c1_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder,dt_c4_6__bagorder,fc1_funct_1,rc1_funct_1,e9_6__bagorder,e1_6__bagorder,e7_6__bagorder,e8_6__bagorder,t6_rfinseq]),
    [interesting(0.8),file(bagorder,e10_6__bagorder),[file(bagorder,e10_6__bagorder)]]).

fof(i3_6__bagorder,theorem,(
    $true ),
    introduced(tautology,[file(bagorder,i3_6__bagorder)]),
    [interesting(0.8),trivial,file(bagorder,i3_6__bagorder)]).

fof(i2_6__bagorder,plain,(
    r1_rfinseq(k5_relat_1(c1_6__bagorder,c3_6__bagorder),k5_relat_1(c2_6__bagorder,c3_6__bagorder)) ),
    inference(conclusion,[status(thm),assumptions([e4_6__bagorder,e1_6__bagorder,dt_c1_6__bagorder,e2_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder,e3_6__bagorder])],[e10_6__bagorder,i3_6__bagorder]),
    [interesting(0.8),file(bagorder,i2_6__bagorder),[file(bagorder,i2_6__bagorder)]]).

fof(i1_6__bagorder,plain,
    ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(c2_6__bagorder)
      & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(c3_6__bagorder))
      & r1_tarski(k2_relat_1(c2_6__bagorder),k1_relat_1(c3_6__bagorder))
      & r1_rfinseq(c1_6__bagorder,c2_6__bagorder) )
   => r1_rfinseq(k5_relat_1(c1_6__bagorder,c3_6__bagorder),k5_relat_1(c2_6__bagorder,c3_6__bagorder)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder]),discharge_asm(discharge,[e1_6__bagorder,e2_6__bagorder,e3_6__bagorder,e4_6__bagorder])],[e1_6__bagorder,e2_6__bagorder,e3_6__bagorder,e4_6__bagorder,i2_6__bagorder]),
    [interesting(0.8),file(bagorder,i1_6__bagorder),[file(bagorder,i1_6__bagorder)]]).

fof(i1_6_tmp__bagorder,plain,
    ( ( v1_relat_1(c1_6__bagorder)
      & v1_funct_1(c1_6__bagorder)
      & v1_relat_1(c2_6__bagorder)
      & v1_funct_1(c2_6__bagorder)
      & v1_relat_1(c3_6__bagorder)
      & v1_funct_1(c3_6__bagorder) )
   => ( ( k1_relat_1(c1_6__bagorder) = k1_relat_1(c2_6__bagorder)
        & r1_tarski(k2_relat_1(c1_6__bagorder),k1_relat_1(c3_6__bagorder))
        & r1_tarski(k2_relat_1(c2_6__bagorder),k1_relat_1(c3_6__bagorder))
        & r1_rfinseq(c1_6__bagorder,c2_6__bagorder) )
     => r1_rfinseq(k5_relat_1(c1_6__bagorder,c3_6__bagorder),k5_relat_1(c2_6__bagorder,c3_6__bagorder)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder])],[dt_c1_6__bagorder,dt_c2_6__bagorder,dt_c3_6__bagorder,i1_6__bagorder]),
    [interesting(1),t4_bagorder]).

fof(t4_bagorder,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( k1_relat_1(A) = k1_relat_1(B)
                  & r1_tarski(k2_relat_1(A),k1_relat_1(C))
                  & r1_tarski(k2_relat_1(B),k1_relat_1(C))
                  & r1_rfinseq(A,B) )
               => r1_rfinseq(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__bagorder,dh_c1_6__bagorder,dh_c2_6__bagorder,dh_c3_6__bagorder]),
    [interesting(1),file(bagorder,t4_bagorder),[file(bagorder,t4_bagorder)]]).