% Mizar ND problem: t39_prepower,prepower,918,52 
fof(dh_c1_39__prepower,definition,
    ( ( v1_xreal_0(c1_39__prepower)
     => ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(0,c1_39__prepower)
              & r1_xreal_0(1,A) )
           => ( r1_xreal_0(1,c1_39__prepower)
              | ( r1_xreal_0(c1_39__prepower,k4_prepower(A,c1_39__prepower))
                & ~ r1_xreal_0(1,k4_prepower(A,c1_39__prepower)) ) ) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ( ( r1_xreal_0(0,B)
                & r1_xreal_0(1,C) )
             => ( r1_xreal_0(1,B)
                | ( r1_xreal_0(B,k4_prepower(C,B))
                  & ~ r1_xreal_0(1,k4_prepower(C,B)) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_39__prepower),file(prepower,c1_39__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_39__prepower)]).

fof(dh_c2_39__prepower,definition,
    ( ( m2_subset_1(c2_39__prepower,k1_numbers,k5_numbers)
     => ( ( r1_xreal_0(0,c1_39__prepower)
          & r1_xreal_0(1,c2_39__prepower) )
       => ( r1_xreal_0(1,c1_39__prepower)
          | ( r1_xreal_0(c1_39__prepower,k4_prepower(c2_39__prepower,c1_39__prepower))
            & ~ r1_xreal_0(1,k4_prepower(c2_39__prepower,c1_39__prepower)) ) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(0,c1_39__prepower)
            & r1_xreal_0(1,A) )
         => ( r1_xreal_0(1,c1_39__prepower)
            | ( r1_xreal_0(c1_39__prepower,k4_prepower(A,c1_39__prepower))
              & ~ r1_xreal_0(1,k4_prepower(A,c1_39__prepower)) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_39__prepower),file(prepower,c2_39__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_39__prepower)]).

fof(e1_39__prepower,assumption,
    ( r1_xreal_0(0,c1_39__prepower)
    & ~ r1_xreal_0(1,c1_39__prepower) ),
    introduced(assumption,[file(prepower,e1_39__prepower)]),
    [interesting(0.8),axiom,file(prepower,e1_39__prepower)]).

fof(e2_39__prepower,assumption,(
    r1_xreal_0(1,c2_39__prepower) ),
    introduced(assumption,[file(prepower,e2_39__prepower)]),
    [interesting(0.8),axiom,file(prepower,e2_39__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(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(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_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

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(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(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(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_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_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_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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

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_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_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(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_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_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_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(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

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

fof(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_newton,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v4_ordinal2(B) )
     => ( v1_xcmplx_0(k2_newton(A,B))
        & v1_xreal_0(k2_newton(A,B)) ) ) ),
    file(newton,fc1_newton),
    [interesting(0.9),axiom,file(newton,fc1_newton)]).

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_newton,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_newton(A,B))
        & v1_xcmplx_0(k2_newton(A,B))
        & v1_xreal_0(k2_newton(A,B))
        & ~ v3_xreal_0(k2_newton(A,B))
        & v1_int_1(k2_newton(A,B)) ) ) ),
    file(newton,fc2_newton),
    [interesting(0.9),axiom,file(newton,fc2_newton)]).

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

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

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

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

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_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(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_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_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

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

fof(dt_k2_newton,axiom,(
    $true ),
    file(newton,k2_newton),
    [interesting(0.9),axiom,file(newton,k2_newton)]).

fof(dt_k4_prepower,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k4_prepower(A,B)) ) ),
    file(prepower,k4_prepower),
    [interesting(0.9),axiom,file(prepower,k4_prepower)]).

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

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_c1_39__prepower,assumption,(
    v1_xreal_0(c1_39__prepower) ),
    introduced(assumption,[file(prepower,c1_39__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_39__prepower)]).

fof(dt_c2_39__prepower,assumption,(
    m2_subset_1(c2_39__prepower,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(prepower,c2_39__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_39__prepower)]).

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(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(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,(
    ~ r1_xreal_0(1,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]).

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(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

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

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

fof(e1_39_2_1_1__prepower,assumption,(
    ~ r1_xreal_0(c1_39__prepower,0) ),
    introduced(assumption,[file(prepower,e1_39_2_1_1__prepower)]),
    [interesting(0.35),axiom,file(prepower,e1_39_2_1_1__prepower)]).

fof(t22_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ( r1_xreal_0(A,1)
              & r1_xreal_0(1,B) )
           => ( r1_xreal_0(A,0)
              | r1_xreal_0(k2_newton(A,B),A) ) ) ) ) ),
    file(prepower,t22_prepower),
    [interesting(0.9),axiom,file(prepower,t22_prepower)]).

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

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(e2_39_2_1_1__prepower,plain,(
    r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_2_1_1__prepower,e1_39__prepower,e2_39__prepower])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_rat_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,rc1_rat_1,rc2_nat_1,rc2_rat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_rat_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc2_membered,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k2_newton,dt_c1_39__prepower,dt_c2_39__prepower,cc1_xreal_0,cc2_xreal_0,cc3_int_1,cc3_nat_1,fc1_newton,fc2_newton,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_39_2_1_1__prepower,e1_39__prepower,e2_39__prepower,t22_prepower,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.35),file(prepower,e2_39_2_1_1__prepower),[file(prepower,e2_39_2_1_1__prepower)]]).

fof(i2_39_2_1_1__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i2_39_2_1_1__prepower)]),
    [interesting(0.35),trivial,file(prepower,i2_39_2_1_1__prepower)]).

fof(i1_39_2_1_1__prepower,plain,(
    r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_2_1_1__prepower,e1_39__prepower,e2_39__prepower])],[e2_39_2_1_1__prepower,i2_39_2_1_1__prepower]),
    [interesting(0.35),file(prepower,i1_39_2_1_1__prepower),[file(prepower,i1_39_2_1_1__prepower)]]).

fof(i1_39_2_1__prepower,plain,
    ( ~ r1_xreal_0(c1_39__prepower,0)
   => r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39__prepower,e2_39__prepower]),discharge_asm(discharge,[e1_39_2_1_1__prepower])],[e1_39_2_1_1__prepower,i1_39_2_1_1__prepower]),
    [interesting(0.5),file(prepower,i1_39_2_1__prepower),[file(prepower,i1_39_2_1__prepower)]]).

fof(e1_39_2_1_2__prepower,assumption,(
    c1_39__prepower = 0 ),
    introduced(assumption,[file(prepower,e1_39_2_1_2__prepower)]),
    [interesting(0.35),axiom,file(prepower,e1_39_2_1_2__prepower)]).

fof(redefinition_k3_newton,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & v4_ordinal2(B) )
     => k3_newton(A,B) = k2_newton(A,B) ) ),
    file(newton,k3_newton),
    [interesting(0.9),axiom,file(newton,k3_newton)]).

fof(dt_k3_newton,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & v4_ordinal2(B) )
     => m1_subset_1(k3_newton(A,B),k1_numbers) ) ),
    file(newton,k3_newton),
    [interesting(0.9),axiom,file(newton,k3_newton)]).

fof(t16_newton,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( r1_xreal_0(1,A)
       => k3_newton(0,A) = 0 ) ) ),
    file(newton,t16_newton),
    [interesting(0.9),axiom,file(newton,t16_newton)]).

fof(e2_39_2_1_2__prepower,plain,(
    r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_2_1_2__prepower,e2_39__prepower])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_rat_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,rc1_rat_1,rc2_nat_1,rc2_rat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_rat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_newton,fc2_membered,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_newton,dt_k2_newton,dt_k3_newton,dt_c1_39__prepower,dt_c2_39__prepower,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc2_newton,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_39_2_1_2__prepower,e2_39__prepower,t16_newton,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.35),file(prepower,e2_39_2_1_2__prepower),[file(prepower,e2_39_2_1_2__prepower)]]).

fof(i2_39_2_1_2__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i2_39_2_1_2__prepower)]),
    [interesting(0.35),trivial,file(prepower,i2_39_2_1_2__prepower)]).

fof(i1_39_2_1_2__prepower,plain,(
    r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_2_1_2__prepower,e2_39__prepower])],[e2_39_2_1_2__prepower,i2_39_2_1_2__prepower]),
    [interesting(0.35),file(prepower,i1_39_2_1_2__prepower),[file(prepower,i1_39_2_1_2__prepower)]]).

fof(i2_39_2_1__prepower,plain,
    ( c1_39__prepower = 0
   => r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e2_39__prepower]),discharge_asm(discharge,[e1_39_2_1_2__prepower])],[e1_39_2_1_2__prepower,i1_39_2_1_2__prepower]),
    [interesting(0.5),file(prepower,i2_39_2_1__prepower),[file(prepower,i2_39_2_1__prepower)]]).

fof(e1_39_2_1__prepower,plain,(
    ~ ( r1_xreal_0(c1_39__prepower,0)
      & c1_39__prepower != 0 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,e1_39__prepower])],[reflexivity_r1_tarski,cc1_rat_1,rc1_rat_1,rc2_rat_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_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,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_39__prepower,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_39__prepower]),
    [interesting(0.5),file(prepower,e1_39_2_1__prepower),[file(prepower,e1_39_2_1__prepower)]]).

fof(e4_39__prepower,plain,(
    r1_xreal_0(k2_newton(c1_39__prepower,c2_39__prepower),c1_39__prepower) ),
    inference(percases,[status(thm),assumptions([dt_c2_39__prepower,e2_39__prepower,dt_c1_39__prepower,e1_39__prepower])],[i1_39_2_1__prepower,i2_39_2_1__prepower,e1_39_2_1__prepower]),
    [interesting(0.8),file(prepower,e4_39__prepower),[file(prepower,e4_39__prepower)]]).

fof(e1_39_1_1_1__prepower,assumption,(
    ~ r1_xreal_0(c1_39__prepower,0) ),
    introduced(assumption,[file(prepower,e1_39_1_1_1__prepower)]),
    [interesting(0.35),axiom,file(prepower,e1_39_1_1_1__prepower)]).

fof(t13_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k2_newton(A,B),0) ) ) ) ),
    file(prepower,t13_prepower),
    [interesting(0.9),axiom,file(prepower,t13_prepower)]).

fof(e2_39_1_1_1__prepower,plain,(
    r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_1_1_1__prepower])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_rat_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,rc1_rat_1,rc2_nat_1,rc2_rat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_rat_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc2_membered,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k2_newton,dt_c1_39__prepower,dt_c2_39__prepower,cc1_xreal_0,cc2_xreal_0,cc3_int_1,cc3_nat_1,fc1_newton,fc2_newton,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e1_39_1_1_1__prepower,t13_prepower]),
    [interesting(0.35),file(prepower,e2_39_1_1_1__prepower),[file(prepower,e2_39_1_1_1__prepower)]]).

fof(i2_39_1_1_1__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i2_39_1_1_1__prepower)]),
    [interesting(0.35),trivial,file(prepower,i2_39_1_1_1__prepower)]).

fof(i1_39_1_1_1__prepower,plain,(
    r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_1_1_1__prepower])],[e2_39_1_1_1__prepower,i2_39_1_1_1__prepower]),
    [interesting(0.35),file(prepower,i1_39_1_1_1__prepower),[file(prepower,i1_39_1_1_1__prepower)]]).

fof(i1_39_1_1__prepower,plain,
    ( ~ r1_xreal_0(c1_39__prepower,0)
   => r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower]),discharge_asm(discharge,[e1_39_1_1_1__prepower])],[e1_39_1_1_1__prepower,i1_39_1_1_1__prepower]),
    [interesting(0.5),file(prepower,i1_39_1_1__prepower),[file(prepower,i1_39_1_1__prepower)]]).

fof(e1_39_1_1_2__prepower,assumption,(
    c1_39__prepower = 0 ),
    introduced(assumption,[file(prepower,e1_39_1_1_2__prepower)]),
    [interesting(0.35),axiom,file(prepower,e1_39_1_1_2__prepower)]).

fof(e2_39_1_1_2__prepower,plain,(
    r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_1_1_2__prepower,e2_39__prepower])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_rat_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,rc1_rat_1,rc2_nat_1,rc2_rat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_rat_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_newton,fc2_membered,rc1_int_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_newton,dt_k2_newton,dt_k3_newton,dt_c1_39__prepower,dt_c2_39__prepower,cc1_xreal_0,cc3_int_1,cc3_nat_1,fc2_newton,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_39_1_1_2__prepower,e2_39__prepower,t16_newton,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.35),file(prepower,e2_39_1_1_2__prepower),[file(prepower,e2_39_1_1_2__prepower)]]).

fof(i2_39_1_1_2__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i2_39_1_1_2__prepower)]),
    [interesting(0.35),trivial,file(prepower,i2_39_1_1_2__prepower)]).

fof(i1_39_1_1_2__prepower,plain,(
    r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39_1_1_2__prepower,e2_39__prepower])],[e2_39_1_1_2__prepower,i2_39_1_1_2__prepower]),
    [interesting(0.35),file(prepower,i1_39_1_1_2__prepower),[file(prepower,i1_39_1_1_2__prepower)]]).

fof(i2_39_1_1__prepower,plain,
    ( c1_39__prepower = 0
   => r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e2_39__prepower]),discharge_asm(discharge,[e1_39_1_1_2__prepower])],[e1_39_1_1_2__prepower,i1_39_1_1_2__prepower]),
    [interesting(0.5),file(prepower,i2_39_1_1__prepower),[file(prepower,i2_39_1_1__prepower)]]).

fof(e1_39_1_1__prepower,plain,(
    ~ ( r1_xreal_0(c1_39__prepower,0)
      & c1_39__prepower != 0 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,e1_39__prepower])],[reflexivity_r1_tarski,cc1_rat_1,rc1_rat_1,rc2_rat_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_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,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_39__prepower,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_39__prepower]),
    [interesting(0.5),file(prepower,e1_39_1_1__prepower),[file(prepower,e1_39_1_1__prepower)]]).

fof(e3_39__prepower,plain,(
    r1_xreal_0(0,k2_newton(c1_39__prepower,c2_39__prepower)) ),
    inference(percases,[status(thm),assumptions([dt_c2_39__prepower,e2_39__prepower,dt_c1_39__prepower,e1_39__prepower])],[i1_39_1_1__prepower,i2_39_1_1__prepower,e1_39_1_1__prepower]),
    [interesting(0.8),file(prepower,e3_39__prepower),[file(prepower,e3_39__prepower)]]).

fof(t36_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_xreal_0(0,A)
                  & r1_xreal_0(A,B)
                  & r1_xreal_0(1,C) )
               => r1_xreal_0(k4_prepower(C,A),k4_prepower(C,B)) ) ) ) ) ),
    file(prepower,t36_prepower),
    [interesting(0.9),axiom,file(prepower,t36_prepower)]).

fof(e5_39__prepower,plain,(
    r1_xreal_0(k4_prepower(c2_39__prepower,k2_newton(c1_39__prepower,c2_39__prepower)),k4_prepower(c2_39__prepower,c1_39__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_39__prepower,e2_39__prepower,dt_c1_39__prepower,e1_39__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,cc20_membered,cc2_membered,cc2_rat_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc6_membered,rc1_int_1,rc1_membered,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_xreal_0,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_newton,fc1_ordinal2,fc2_newton,fc5_membered,rc1_nat_1,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_newton,dt_k4_prepower,dt_k5_numbers,dt_m2_subset_1,dt_c1_39__prepower,dt_c2_39__prepower,cc2_xreal_0,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_39__prepower,e2_39__prepower,e3_39__prepower,t36_prepower,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(prepower,e5_39__prepower),[file(prepower,e5_39__prepower)]]).

fof(t28_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(1,B) )
           => ( k2_newton(k4_prepower(B,A),B) = A
              & k4_prepower(B,k2_newton(A,B)) = A ) ) ) ) ),
    file(prepower,t28_prepower),
    [interesting(0.9),axiom,file(prepower,t28_prepower)]).

fof(e6_39__prepower,plain,(
    r1_xreal_0(c1_39__prepower,k4_prepower(c2_39__prepower,c1_39__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_39__prepower,dt_c1_39__prepower,e1_39__prepower,e2_39__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,cc20_membered,cc2_membered,cc2_rat_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc6_membered,rc1_int_1,rc1_membered,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_xreal_0,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_newton,fc1_ordinal2,fc2_newton,fc5_membered,rc1_nat_1,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_newton,dt_k4_prepower,dt_k5_numbers,dt_m2_subset_1,dt_c1_39__prepower,dt_c2_39__prepower,cc2_xreal_0,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e5_39__prepower,e1_39__prepower,e2_39__prepower,t28_prepower,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(prepower,e6_39__prepower),[file(prepower,e6_39__prepower)]]).

fof(redefinition_k5_prepower,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_prepower(A,B) = k4_prepower(A,B) ) ),
    file(prepower,k5_prepower),
    [interesting(0.9),axiom,file(prepower,k5_prepower)]).

fof(dt_k5_prepower,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k5_prepower(A,B),k1_numbers) ) ),
    file(prepower,k5_prepower),
    [interesting(0.9),axiom,file(prepower,k5_prepower)]).

fof(t37_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r1_xreal_0(0,A)
                  & ~ r1_xreal_0(B,A)
                  & r1_xreal_0(1,C)
                  & r1_xreal_0(k4_prepower(C,B),k4_prepower(C,A)) ) ) ) ) ),
    file(prepower,t37_prepower),
    [interesting(0.9),axiom,file(prepower,t37_prepower)]).

fof(e7_39__prepower,plain,(
    ~ r1_xreal_0(k5_prepower(c2_39__prepower,1),k4_prepower(c2_39__prepower,c1_39__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39__prepower,e2_39__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,cc20_membered,cc2_membered,cc2_rat_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc6_membered,rc1_int_1,rc1_membered,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_xreal_0,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,rc1_nat_1,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k5_prepower,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_prepower,dt_k5_numbers,dt_k5_prepower,dt_m2_subset_1,dt_c1_39__prepower,dt_c2_39__prepower,cc2_xreal_0,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_39__prepower,e2_39__prepower,t37_prepower,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(prepower,e7_39__prepower),[file(prepower,e7_39__prepower)]]).

fof(t29_prepower,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_xreal_0(1,A)
       => k5_prepower(A,1) = 1 ) ) ),
    file(prepower,t29_prepower),
    [interesting(0.9),axiom,file(prepower,t29_prepower)]).

fof(e8_39__prepower,plain,(
    ~ r1_xreal_0(1,k4_prepower(c2_39__prepower,c1_39__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39__prepower,e2_39__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,cc20_membered,cc2_membered,cc2_rat_1,cc3_membered,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_xreal_0,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k5_prepower,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_prepower,dt_k5_numbers,dt_k5_prepower,dt_m2_subset_1,dt_c1_39__prepower,dt_c2_39__prepower,fc2_membered,spc1_numerals,spc1_boole,e7_39__prepower,e2_39__prepower,t29_prepower,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(prepower,e8_39__prepower),[file(prepower,e8_39__prepower)]]).

fof(i5_39__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i5_39__prepower)]),
    [interesting(0.8),trivial,file(prepower,i5_39__prepower)]).

fof(i4_39__prepower,plain,(
    ~ r1_xreal_0(1,k4_prepower(c2_39__prepower,c1_39__prepower)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39__prepower,e2_39__prepower])],[e8_39__prepower,i5_39__prepower]),
    [interesting(0.8),file(prepower,i4_39__prepower),[file(prepower,i4_39__prepower)]]).

fof(i3_39__prepower,plain,
    ( r1_xreal_0(c1_39__prepower,k4_prepower(c2_39__prepower,c1_39__prepower))
    & ~ r1_xreal_0(1,k4_prepower(c2_39__prepower,c1_39__prepower)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower,e1_39__prepower,e2_39__prepower])],[e6_39__prepower,i4_39__prepower]),
    [interesting(0.8),file(prepower,i3_39__prepower),[file(prepower,i3_39__prepower)]]).

fof(i2_39__prepower,plain,
    ( ( r1_xreal_0(0,c1_39__prepower)
      & r1_xreal_0(1,c2_39__prepower) )
   => ( r1_xreal_0(1,c1_39__prepower)
      | ( r1_xreal_0(c1_39__prepower,k4_prepower(c2_39__prepower,c1_39__prepower))
        & ~ r1_xreal_0(1,k4_prepower(c2_39__prepower,c1_39__prepower)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_39__prepower,dt_c2_39__prepower]),discharge_asm(discharge,[e1_39__prepower,e2_39__prepower])],[e1_39__prepower,e2_39__prepower,i3_39__prepower]),
    [interesting(0.8),file(prepower,i2_39__prepower),[file(prepower,i2_39__prepower)]]).

fof(i2_39_tmp__prepower,plain,
    ( m2_subset_1(c2_39__prepower,k1_numbers,k5_numbers)
   => ( ( r1_xreal_0(0,c1_39__prepower)
        & r1_xreal_0(1,c2_39__prepower) )
     => ( r1_xreal_0(1,c1_39__prepower)
        | ( r1_xreal_0(c1_39__prepower,k4_prepower(c2_39__prepower,c1_39__prepower))
          & ~ r1_xreal_0(1,k4_prepower(c2_39__prepower,c1_39__prepower)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_39__prepower]),discharge_asm(discharge,[dt_c2_39__prepower])],[dt_c2_39__prepower,i2_39__prepower]),
    [interesting(0.8),i1_39__prepower]).

fof(i1_39__prepower,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( ( r1_xreal_0(0,c1_39__prepower)
          & r1_xreal_0(1,A) )
       => ( r1_xreal_0(1,c1_39__prepower)
          | ( r1_xreal_0(c1_39__prepower,k4_prepower(A,c1_39__prepower))
            & ~ r1_xreal_0(1,k4_prepower(A,c1_39__prepower)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_39__prepower])],[i2_39_tmp__prepower,dh_c2_39__prepower]),
    [interesting(0.8),file(prepower,i1_39__prepower),[file(prepower,i1_39__prepower)]]).

fof(i1_39_tmp__prepower,plain,
    ( v1_xreal_0(c1_39__prepower)
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(0,c1_39__prepower)
            & r1_xreal_0(1,A) )
         => ( r1_xreal_0(1,c1_39__prepower)
            | ( r1_xreal_0(c1_39__prepower,k4_prepower(A,c1_39__prepower))
              & ~ r1_xreal_0(1,k4_prepower(A,c1_39__prepower)) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_39__prepower])],[dt_c1_39__prepower,i1_39__prepower]),
    [interesting(1),t39_prepower]).

fof(t39_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(1,B) )
           => ( r1_xreal_0(1,A)
              | ( r1_xreal_0(A,k4_prepower(B,A))
                & ~ r1_xreal_0(1,k4_prepower(B,A)) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_39_tmp__prepower,dh_c1_39__prepower]),
    [interesting(1),file(prepower,t39_prepower),[file(prepower,t39_prepower)]]).