% Mizar ND problem: t3_prepower,prepower,79,54 
fof(dh_c1_5__prepower,definition,
    ( ( v1_xreal_0(c1_5__prepower)
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,k5_numbers,k1_numbers)
            & m2_relset_1(A,k5_numbers,k1_numbers) )
         => ( ( v4_seq_2(A)
              & ! [B] : 
                  ( m2_subset_1(B,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),c1_5__prepower) ) )
           => r1_xreal_0(k2_seq_2(A),c1_5__prepower) ) ) )
   => ! [C] : 
        ( v1_xreal_0(C)
       => ! [D] : 
            ( ( v1_funct_1(D)
              & v1_funct_2(D,k5_numbers,k1_numbers)
              & m2_relset_1(D,k5_numbers,k1_numbers) )
           => ( ( v4_seq_2(D)
                & ! [E] : 
                    ( m2_subset_1(E,k1_numbers,k5_numbers)
                   => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,D,E),C) ) )
             => r1_xreal_0(k2_seq_2(D),C) ) ) ) ),
    introduced(definition,[new_symbol(c1_5__prepower),file(prepower,c1_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_5__prepower)]).

fof(dh_c2_5__prepower,definition,
    ( ( ( v1_funct_1(c2_5__prepower)
        & v1_funct_2(c2_5__prepower,k5_numbers,k1_numbers)
        & m2_relset_1(c2_5__prepower,k5_numbers,k1_numbers) )
     => ( ( v4_seq_2(c2_5__prepower)
          & ! [A] : 
              ( m2_subset_1(A,k1_numbers,k5_numbers)
             => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,A),c1_5__prepower) ) )
       => r1_xreal_0(k2_seq_2(c2_5__prepower),c1_5__prepower) ) )
   => ! [B] : 
        ( ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & m2_relset_1(B,k5_numbers,k1_numbers) )
       => ( ( v4_seq_2(B)
            & ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),c1_5__prepower) ) )
         => r1_xreal_0(k2_seq_2(B),c1_5__prepower) ) ) ),
    introduced(definition,[new_symbol(c2_5__prepower),file(prepower,c2_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_5__prepower)]).

fof(e1_5__prepower,assumption,(
    v4_seq_2(c2_5__prepower) ),
    introduced(assumption,[file(prepower,e1_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,e1_5__prepower)]).

fof(e2_5__prepower,assumption,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,A),c1_5__prepower) ) ),
    introduced(assumption,[file(prepower,e2_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,e2_5__prepower)]).

fof(cc1_rat_1,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(rat_1,cc1_rat_1),
    [interesting(0.9),axiom,file(rat_1,cc1_rat_1)]).

fof(cc4_seqm_3,theorem,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v3_seqm_3(A)
          & v4_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v5_seqm_3(A) ) ) ) ),
    file(seqm_3,cc4_seqm_3),
    [interesting(0.9),axiom,file(seqm_3,cc4_seqm_3)]).

fof(rc1_rat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_rat_1(A) ) ),
    file(rat_1,rc1_rat_1),
    [interesting(0.9),axiom,file(rat_1,rc1_rat_1)]).

fof(rc2_rat_1,theorem,(
    ? [A] : v1_rat_1(A) ),
    file(rat_1,rc2_rat_1),
    [interesting(0.9),axiom,file(rat_1,rc2_rat_1)]).

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

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(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

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(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc2_rat_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v1_rat_1(A) ) ) ),
    file(rat_1,cc2_rat_1),
    [interesting(0.9),axiom,file(rat_1,cc2_rat_1)]).

fof(cc3_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    [interesting(0.9),axiom,file(int_1,cc3_int_1)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

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_seqm_3,theorem,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v5_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v3_seqm_3(A)
          & v4_seqm_3(A) ) ) ) ),
    file(seqm_3,cc3_seqm_3),
    [interesting(0.9),axiom,file(seqm_3,cc3_seqm_3)]).

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_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    [interesting(0.9),axiom,file(int_1,cc4_int_1)]).

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(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(fc1_seq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_xcmplx_0(k1_funct_1(A,B))
        & v1_xreal_0(k1_funct_1(A,B)) ) ) ),
    file(seq_1,fc1_seq_1),
    [interesting(0.9),axiom,file(seq_1,fc1_seq_1)]).

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(fc6_membered,theorem,
    ( v1_xboole_0(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) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_int_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    [interesting(0.9),axiom,file(int_1,rc1_int_1)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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_seq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A) ) ),
    file(seq_1,rc1_seq_1),
    [interesting(0.9),axiom,file(seq_1,rc1_seq_1)]).

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

fof(rc2_int_1,theorem,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    [interesting(0.9),axiom,file(int_1,rc2_int_1)]).

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

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

fof(rc3_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_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

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

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

fof(dt_k1_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => v1_xreal_0(k1_seq_2(A)) ) ),
    file(seq_2,k1_seq_2),
    [interesting(0.9),axiom,file(seq_2,k1_seq_2)]).

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

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

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

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

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(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc1_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

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

fof(cc1_seq_1,theorem,(
    ! [A,B] : 
      ( v2_membered(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( v1_funct_1(C)
           => ( v1_funct_1(C)
              & v1_seq_1(C) ) ) ) ) ),
    file(seq_1,cc1_seq_1),
    [interesting(0.9),axiom,file(seq_1,cc1_seq_1)]).

fof(cc2_int_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_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    [interesting(0.9),axiom,file(int_1,cc2_int_1)]).

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

fof(cc2_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(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

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(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

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(fc2_seqm_3,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B))
      & v5_seqm_3(k2_funcop_1(A,B)) ) ),
    file(seqm_3,fc2_seqm_3),
    [interesting(0.9),axiom,file(seqm_3,fc2_seqm_3)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

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(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(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(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(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_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_k2_seq_2,definition,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => k2_seq_2(A) = k1_seq_2(A) ) ),
    file(seq_2,k2_seq_2),
    [interesting(0.9),axiom,file(seq_2,k2_seq_2)]).

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

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

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_k2_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k2_seq_2(A),k1_numbers) ) ),
    file(seq_2,k2_seq_2),
    [interesting(0.9),axiom,file(seq_2,k2_seq_2)]).

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_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_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_5__prepower,assumption,(
    v1_xreal_0(c1_5__prepower) ),
    introduced(assumption,[file(prepower,c1_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_5__prepower)]).

fof(dt_c2_5__prepower,assumption,
    ( v1_funct_1(c2_5__prepower)
    & v1_funct_2(c2_5__prepower,k5_numbers,k1_numbers)
    & m2_relset_1(c2_5__prepower,k5_numbers,k1_numbers) ),
    introduced(assumption,[file(prepower,c2_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_5__prepower)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(de_c3_5__prepower,definition,(
    c3_5__prepower = k2_funcop_1(k5_numbers,c1_5__prepower) ),
    introduced(definition,[new_symbol(c3_5__prepower),file(prepower,c3_5__prepower)]),
    [interesting(0.8),axiom,file(prepower,c3_5__prepower)]).

fof(d1_xreal_0,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
    <=> r2_hidden(A,k1_numbers) ) ),
    file(xreal_0,d1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,d1_xreal_0)]).

fof(e3_5__prepower,plain,(
    r2_hidden(c1_5__prepower,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,cc1_xreal_0,cc2_rat_1,cc3_int_1,cc3_nat_1,cc4_int_1,rc1_int_1,rc1_nat_1,rc1_rat_1,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,cc7_xreal_0,rc1_xreal_0,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_c1_5__prepower,cc2_xreal_0,fc2_membered,t1_subset,t7_boole,d1_xreal_0]),
    [interesting(0.8),file(prepower,e3_5__prepower),[file(prepower,e3_5__prepower)]]).

fof(t57_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,B)
     => ( v1_funct_1(k2_funcop_1(A,C))
        & v1_funct_2(k2_funcop_1(A,C),A,B)
        & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ),
    file(funcop_1,t57_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t57_funcop_1)]).

fof(e4_5__prepower,plain,
    ( v1_funct_1(k2_funcop_1(k5_numbers,c1_5__prepower))
    & v1_funct_2(k2_funcop_1(k5_numbers,c1_5__prepower),k5_numbers,k1_numbers)
    & m2_relset_1(k2_funcop_1(k5_numbers,c1_5__prepower),k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_seqm_3,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k2_funcop_1,dt_k5_numbers,dt_m2_relset_1,dt_c1_5__prepower,fc2_membered,fc2_seqm_3,t1_subset,t7_boole,e3_5__prepower,t57_funcop_1]),
    [interesting(0.8),file(prepower,e4_5__prepower),[file(prepower,e4_5__prepower)]]).

fof(dt_c3_5__prepower,plain,
    ( v1_funct_1(c3_5__prepower)
    & v1_funct_2(c3_5__prepower,k5_numbers,k1_numbers)
    & m2_relset_1(c3_5__prepower,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_seqm_3,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k2_funcop_1,dt_k5_numbers,dt_m2_relset_1,dt_c1_5__prepower,fc2_membered,fc2_seqm_3,de_c3_5__prepower,e4_5__prepower]),
    [interesting(0.8),file(prepower,c3_5__prepower),[file(prepower,c3_5__prepower)]]).

fof(dh_c1_5_2__prepower,definition,
    ( ( m2_subset_1(c1_5_2__prepower,k1_numbers,k5_numbers)
     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,c1_5_2__prepower),k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,c1_5_2__prepower)) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,A),k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,A)) ) ),
    introduced(definition,[new_symbol(c1_5_2__prepower),file(prepower,c1_5_2__prepower)]),
    [interesting(0.65),axiom,file(prepower,c1_5_2__prepower)]).

fof(dt_c1_5_2__prepower,assumption,(
    m2_subset_1(c1_5_2__prepower,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(prepower,c1_5_2__prepower)]),
    [interesting(0.65),axiom,file(prepower,c1_5_2__prepower)]).

fof(e1_5_2__prepower,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,c1_5_2__prepower),c1_5__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower,dt_c1_5_2__prepower,dt_c2_5__prepower,e2_5__prepower])],[cc1_rat_1,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5__prepower,dt_c1_5_2__prepower,dt_c2_5__prepower,fc2_membered,e2_5__prepower]),
    [interesting(0.65),file(prepower,e1_5_2__prepower),[file(prepower,e1_5_2__prepower)]]).

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(e5_5__prepower,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,A) = c1_5__prepower ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_seqm_3,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_funcop_1,dt_k2_seq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5__prepower,dt_c3_5__prepower,de_c3_5__prepower,fc2_membered,fc2_seqm_3,t1_subset,t7_boole,t13_funcop_1]),
    [interesting(0.8),file(prepower,e5_5__prepower),[file(prepower,e5_5__prepower)]]).

fof(e2_5_2__prepower,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,c1_5_2__prepower),k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,c1_5_2__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_2__prepower,dt_c2_5__prepower,e2_5__prepower,dt_c1_5__prepower])],[cc1_rat_1,cc4_seqm_3,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_seqm_3,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc2_seqm_3,fc5_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5__prepower,dt_c1_5_2__prepower,dt_c2_5__prepower,dt_c3_5__prepower,de_c3_5__prepower,fc2_membered,e1_5_2__prepower,e5_5__prepower]),
    [interesting(0.65),file(prepower,e2_5_2__prepower),[file(prepower,e2_5_2__prepower)]]).

fof(i2_5_2__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i2_5_2__prepower)]),
    [interesting(0.65),trivial,file(prepower,i2_5_2__prepower)]).

fof(i1_5_2__prepower,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,c1_5_2__prepower),k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,c1_5_2__prepower)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_2__prepower,dt_c2_5__prepower,e2_5__prepower,dt_c1_5__prepower])],[e2_5_2__prepower,i2_5_2__prepower]),
    [interesting(0.65),file(prepower,i1_5_2__prepower),[file(prepower,i1_5_2__prepower)]]).

fof(i1_5_2_tmp__prepower,plain,
    ( m2_subset_1(c1_5_2__prepower,k1_numbers,k5_numbers)
   => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,c1_5_2__prepower),k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,c1_5_2__prepower)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_5__prepower,e2_5__prepower,dt_c1_5__prepower]),discharge_asm(discharge,[dt_c1_5_2__prepower])],[dt_c1_5_2__prepower,i1_5_2__prepower]),
    [interesting(0.8),e8_5__prepower]).

fof(e8_5__prepower,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,A),k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c2_5__prepower,e2_5__prepower,dt_c1_5__prepower])],[i1_5_2_tmp__prepower,dh_c1_5_2__prepower]),
    [interesting(0.8),file(prepower,e8_5__prepower),[file(prepower,e8_5__prepower)]]).

fof(t39_seq_4,theorem,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => v4_seq_2(A) ) ) ),
    file(seq_4,t39_seq_4),
    [interesting(0.9),axiom,file(seq_4,t39_seq_4)]).

fof(e6_5__prepower,plain,(
    v4_seq_2(c3_5__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_rat_1,rc2_rat_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc3_nat_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_c1_5__prepower,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc3_seqm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc2_seqm_3,fc5_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_relset_1,dt_c3_5__prepower,de_c3_5__prepower,fc2_membered,t39_seq_4]),
    [interesting(0.8),file(prepower,e6_5__prepower),[file(prepower,e6_5__prepower)]]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(redefinition_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

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(t41_seq_4,theorem,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_2(A) = k8_funct_2(k5_numbers,k1_numbers,A,B) ) ) ) ),
    file(seq_4,t41_seq_4),
    [interesting(0.9),axiom,file(seq_4,t41_seq_4)]).

fof(e1_5_1__prepower,plain,(
    k2_seq_2(c3_5__prepower) = k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_int_1,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_seq_1,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_c1_5__prepower,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc3_seqm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc2_seqm_3,fc5_membered,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k2_seq_2,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_m2_subset_1,dt_c3_5__prepower,de_c3_5__prepower,fc2_membered,spc0_numerals,spc0_boole,t41_seq_4]),
    [interesting(0.65),file(prepower,e1_5_1__prepower),[file(prepower,e1_5_1__prepower)]]).

fof(e2_5_1__prepower,plain,(
    k2_seq_1(k5_numbers,k1_numbers,c3_5__prepower,0) = c1_5__prepower ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__prepower])],[cc1_rat_1,cc4_seqm_3,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_seqm_3,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_seq_1,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc2_seqm_3,fc5_membered,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5__prepower,dt_c3_5__prepower,de_c3_5__prepower,fc2_membered,spc0_numerals,spc0_boole,e5_5__prepower]),
    [interesting(0.65),file(prepower,e2_5_1__prepower),[file(prepower,e2_5_1__prepower)]]).

fof(e7_5__prepower,plain,(
    k2_seq_2(c3_5__prepower) = c1_5__prepower ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_5__prepower])],[e1_5_1__prepower,e2_5_1__prepower]),
    [interesting(0.8),file(prepower,e7_5__prepower),[file(prepower,e7_5__prepower)]]).

fof(t32_seq_2,theorem,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v4_seq_2(A)
              & v4_seq_2(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,B,C)) ) )
           => r1_xreal_0(k2_seq_2(A),k2_seq_2(B)) ) ) ) ),
    file(seq_2,t32_seq_2),
    [interesting(0.9),axiom,file(seq_2,t32_seq_2)]).

fof(e9_5__prepower,plain,(
    r1_xreal_0(k2_seq_2(c2_5__prepower),c1_5__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__prepower,e2_5__prepower,e1_5__prepower,dt_c1_5__prepower])],[cc1_rat_1,cc4_seqm_3,rc1_rat_1,rc2_rat_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_rat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_seqm_3,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,fc4_ordinal2,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc2_seqm_3,fc5_membered,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k2_seq_2,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c1_5__prepower,dt_c2_5__prepower,dt_c3_5__prepower,de_c3_5__prepower,fc2_membered,e8_5__prepower,e1_5__prepower,e6_5__prepower,e7_5__prepower,t32_seq_2]),
    [interesting(0.8),file(prepower,e9_5__prepower),[file(prepower,e9_5__prepower)]]).

fof(i4_5__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i4_5__prepower)]),
    [interesting(0.8),trivial,file(prepower,i4_5__prepower)]).

fof(i3_5__prepower,plain,(
    r1_xreal_0(k2_seq_2(c2_5__prepower),c1_5__prepower) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_5__prepower,e2_5__prepower,e1_5__prepower,dt_c1_5__prepower])],[e9_5__prepower,i4_5__prepower]),
    [interesting(0.8),file(prepower,i3_5__prepower),[file(prepower,i3_5__prepower)]]).

fof(i2_5__prepower,plain,
    ( ( v4_seq_2(c2_5__prepower)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,A),c1_5__prepower) ) )
   => r1_xreal_0(k2_seq_2(c2_5__prepower),c1_5__prepower) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_5__prepower,dt_c1_5__prepower]),discharge_asm(discharge,[e1_5__prepower,e2_5__prepower])],[e1_5__prepower,e2_5__prepower,i3_5__prepower]),
    [interesting(0.8),file(prepower,i2_5__prepower),[file(prepower,i2_5__prepower)]]).

fof(i2_5_tmp__prepower,plain,
    ( ( v1_funct_1(c2_5__prepower)
      & v1_funct_2(c2_5__prepower,k5_numbers,k1_numbers)
      & m2_relset_1(c2_5__prepower,k5_numbers,k1_numbers) )
   => ( ( v4_seq_2(c2_5__prepower)
        & ! [A] : 
            ( m2_subset_1(A,k1_numbers,k5_numbers)
           => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c2_5__prepower,A),c1_5__prepower) ) )
     => r1_xreal_0(k2_seq_2(c2_5__prepower),c1_5__prepower) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__prepower]),discharge_asm(discharge,[dt_c2_5__prepower])],[dt_c2_5__prepower,i2_5__prepower]),
    [interesting(0.8),i1_5__prepower]).

fof(i1_5__prepower,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( ( v4_seq_2(A)
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),c1_5__prepower) ) )
       => r1_xreal_0(k2_seq_2(A),c1_5__prepower) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__prepower])],[i2_5_tmp__prepower,dh_c2_5__prepower]),
    [interesting(0.8),file(prepower,i1_5__prepower),[file(prepower,i1_5__prepower)]]).

fof(i1_5_tmp__prepower,plain,
    ( v1_xreal_0(c1_5__prepower)
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & m2_relset_1(A,k5_numbers,k1_numbers) )
       => ( ( v4_seq_2(A)
            & ! [B] : 
                ( m2_subset_1(B,k1_numbers,k5_numbers)
               => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),c1_5__prepower) ) )
         => r1_xreal_0(k2_seq_2(A),c1_5__prepower) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__prepower])],[dt_c1_5__prepower,i1_5__prepower]),
    [interesting(1),t3_prepower]).

fof(t3_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v4_seq_2(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,B,C),A) ) )
           => r1_xreal_0(k2_seq_2(B),A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__prepower,dh_c1_5__prepower]),
    [interesting(1),file(prepower,t3_prepower),[file(prepower,t3_prepower)]]).