% Mizar ND problem: t105_prepower,prepower,2995,39 
fof(dh_c1_121__prepower,definition,
    ( ( v1_xreal_0(c1_121__prepower)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ! [B] : 
              ( v1_xreal_0(B)
             => ( ~ r1_xreal_0(c1_121__prepower,0)
               => k12_prepower(k12_prepower(c1_121__prepower,A),B) = k12_prepower(c1_121__prepower,k3_xcmplx_0(A,B)) ) ) ) )
   => ! [C] : 
        ( v1_xreal_0(C)
       => ! [D] : 
            ( v1_xreal_0(D)
           => ! [E] : 
                ( v1_xreal_0(E)
               => ( ~ r1_xreal_0(C,0)
                 => k12_prepower(k12_prepower(C,D),E) = k12_prepower(C,k3_xcmplx_0(D,E)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_121__prepower),file(prepower,c1_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_121__prepower)]).

fof(dh_c2_121__prepower,definition,
    ( ( v1_xreal_0(c2_121__prepower)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ( ~ r1_xreal_0(c1_121__prepower,0)
           => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),A) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,A)) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( v1_xreal_0(C)
           => ( ~ r1_xreal_0(c1_121__prepower,0)
             => k12_prepower(k12_prepower(c1_121__prepower,B),C) = k12_prepower(c1_121__prepower,k3_xcmplx_0(B,C)) ) ) ) ),
    introduced(definition,[new_symbol(c2_121__prepower),file(prepower,c2_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_121__prepower)]).

fof(dh_c3_121__prepower,definition,
    ( ( v1_xreal_0(c3_121__prepower)
     => ( ~ r1_xreal_0(c1_121__prepower,0)
       => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c3_121__prepower) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,c3_121__prepower)) ) )
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ~ r1_xreal_0(c1_121__prepower,0)
         => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),A) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,A)) ) ) ),
    introduced(definition,[new_symbol(c3_121__prepower),file(prepower,c3_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c3_121__prepower)]).

fof(e1_121__prepower,assumption,(
    ~ r1_xreal_0(c1_121__prepower,0) ),
    introduced(assumption,[file(prepower,e1_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,e1_121__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(fc11_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_rat_1(k6_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc11_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc11_rat_1)]).

fof(fc12_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc12_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc12_rat_1)]).

fof(fc14_rat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_rat_1(k6_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc14_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc14_rat_1)]).

fof(fc15_rat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc15_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc15_rat_1)]).

fof(fc16_rat_1,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_rat_1(k4_xcmplx_0(A)) ) ) ),
    file(rat_1,fc16_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc16_rat_1)]).

fof(fc1_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc1_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc1_rat_1)]).

fof(fc3_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_rat_1(k6_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc3_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc3_rat_1)]).

fof(fc5_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_rat_1(k6_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc5_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc5_rat_1)]).

fof(fc6_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc6_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc6_rat_1)]).

fof(fc8_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_rat_1(k6_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc8_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc8_rat_1)]).

fof(fc9_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc9_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc9_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(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(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(fc14_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc14_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc14_xreal_0)]).

fof(fc15_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc15_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc15_xreal_0)]).

fof(fc16_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc16_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc16_xreal_0)]).

fof(fc19_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & ~ v2_xreal_0(k6_xcmplx_0(A,B))
        & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc19_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc19_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(fc20_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v2_xreal_0(k6_xcmplx_0(B,A))
        & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc20_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc20_xreal_0)]).

fof(fc21_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc21_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc21_xreal_0)]).

fof(fc22_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc22_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc22_xreal_0)]).

fof(fc24_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc24_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc24_xreal_0)]).

fof(fc2_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & v1_int_1(k3_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc2_int_1),
    [interesting(0.9),axiom,file(int_1,fc2_int_1)]).

fof(fc2_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc2_nat_1)]).

fof(fc3_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc3_int_1),
    [interesting(0.9),axiom,file(int_1,fc3_int_1)]).

fof(fc4_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc4_int_1),
    [interesting(0.9),axiom,file(int_1,fc4_int_1)]).

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(fc6_seq_1,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => ( v1_relat_1(k12_seq_1(B,A))
        & v1_funct_1(k12_seq_1(B,A))
        & v1_seq_1(k12_seq_1(B,A)) ) ) ),
    file(seq_1,fc6_seq_1),
    [interesting(0.9),axiom,file(seq_1,fc6_seq_1)]).

fof(fc7_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(B,A))
        & v1_xreal_0(k3_xcmplx_0(B,A))
        & v1_int_1(k3_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc7_int_1),
    [interesting(0.9),axiom,file(int_1,fc7_int_1)]).

fof(fc8_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & v1_int_1(k6_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc8_int_1),
    [interesting(0.9),axiom,file(int_1,fc8_int_1)]).

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_prepower,theorem,(
    ? [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v1_seq_1(A)
      & v1_prepower(A) ) ),
    file(prepower,rc1_prepower),
    [interesting(0.9),axiom,file(prepower,rc1_prepower)]).

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(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_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_k12_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_xreal_0(B) )
     => ( v1_relat_1(k12_seq_1(A,B))
        & v1_funct_1(k12_seq_1(A,B)) ) ) ),
    file(seq_1,k12_seq_1),
    [interesting(0.9),axiom,file(seq_1,k12_seq_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_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(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(fc13_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc13_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc13_xreal_0)]).

fof(fc17_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(A,B))
        & v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v2_xreal_0(k6_xcmplx_0(A,B))
        & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc17_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc17_xreal_0)]).

fof(fc18_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k6_xcmplx_0(B,A))
        & v1_xcmplx_0(k6_xcmplx_0(B,A))
        & v1_xreal_0(k6_xcmplx_0(B,A))
        & ~ v2_xreal_0(k6_xcmplx_0(B,A))
        & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc18_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc18_xreal_0)]).

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(fc23_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B))
        & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc23_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc23_xreal_0)]).

fof(fc5_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A))
        & v1_int_1(k4_xcmplx_0(A)) ) ) ),
    file(int_1,fc5_int_1),
    [interesting(0.9),axiom,file(int_1,fc5_int_1)]).

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(fc9_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B))
        & v1_int_1(k6_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc9_int_1),
    [interesting(0.9),axiom,file(int_1,fc9_int_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(spc2_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) ),
    file(arithm,spc2_arithm),
    [interesting(0.9),axiom,file(arithm,spc2_arithm)]).

fof(spc7_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_arithm)]).

fof(spc9_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ),
    file(arithm,spc9_arithm),
    [interesting(0.9),axiom,file(arithm,spc9_arithm)]).

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_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    [interesting(0.9),axiom,file(arithm,t2_arithm)]).

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_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(1,A) = A ) ),
    file(arithm,t3_arithm),
    [interesting(0.9),axiom,file(arithm,t3_arithm)]).

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_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    [interesting(0.9),axiom,file(arithm,t4_arithm)]).

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(commutativity_k3_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(involutiveness_k4_xcmplx_0,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

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_k14_seq_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_xreal_0(B) )
     => k14_seq_1(A,B) = k12_seq_1(A,B) ) ),
    file(seq_1,k14_seq_1),
    [interesting(0.9),axiom,file(seq_1,k14_seq_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_k11_prepower,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & v1_prepower(B)
        & m1_relset_1(B,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k11_prepower(A,B))
        & v1_funct_2(k11_prepower(A,B),k5_numbers,k1_numbers)
        & m2_relset_1(k11_prepower(A,B),k5_numbers,k1_numbers) ) ) ),
    file(prepower,k11_prepower),
    [interesting(0.9),axiom,file(prepower,k11_prepower)]).

fof(dt_k12_prepower,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k12_prepower(A,B)) ) ),
    file(prepower,k12_prepower),
    [interesting(0.9),axiom,file(prepower,k12_prepower)]).

fof(dt_k14_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_xreal_0(B) )
     => ( v1_funct_1(k14_seq_1(A,B))
        & v1_funct_2(k14_seq_1(A,B),k5_numbers,k1_numbers)
        & m2_relset_1(k14_seq_1(A,B),k5_numbers,k1_numbers) ) ) ),
    file(seq_1,k14_seq_1),
    [interesting(0.9),axiom,file(seq_1,k14_seq_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_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]).

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_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]).

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_121__prepower,assumption,(
    v1_xreal_0(c1_121__prepower) ),
    introduced(assumption,[file(prepower,c1_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_121__prepower)]).

fof(dt_c2_121__prepower,assumption,(
    v1_xreal_0(c2_121__prepower) ),
    introduced(assumption,[file(prepower,c2_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_121__prepower)]).

fof(dt_c3_121__prepower,assumption,(
    v1_xreal_0(c3_121__prepower) ),
    introduced(assumption,[file(prepower,c3_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c3_121__prepower)]).

fof(dh_c4_121__prepower,definition,
    ( ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_prepower(A)
        & m2_relset_1(A,k5_numbers,k1_numbers)
        & v4_seq_2(A)
        & c3_121__prepower = k2_seq_2(A)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => r1_xreal_0(k10_prepower(A,B),c3_121__prepower) ) )
   => ( v1_funct_1(c4_121__prepower)
      & v1_funct_2(c4_121__prepower,k5_numbers,k1_numbers)
      & v1_prepower(c4_121__prepower)
      & m2_relset_1(c4_121__prepower,k5_numbers,k1_numbers)
      & v4_seq_2(c4_121__prepower)
      & c3_121__prepower = k2_seq_2(c4_121__prepower)
      & ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => r1_xreal_0(k10_prepower(c4_121__prepower,C),c3_121__prepower) ) ) ),
    introduced(definition,[new_symbol(c4_121__prepower),file(prepower,c4_121__prepower)]),
    [interesting(0.8),axiom,file(prepower,c4_121__prepower)]).

fof(redefinition_k10_prepower,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_prepower(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k10_prepower(A,B) = k1_funct_1(A,B) ) ),
    file(prepower,k10_prepower),
    [interesting(0.9),axiom,file(prepower,k10_prepower)]).

fof(dt_k10_prepower,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & v1_prepower(A)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & m1_subset_1(B,k5_numbers) )
     => v1_rat_1(k10_prepower(A,B)) ) ),
    file(prepower,k10_prepower),
    [interesting(0.9),axiom,file(prepower,k10_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(t79_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ? [B] : 
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & v1_prepower(B)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & v4_seq_2(B)
          & k2_seq_2(B) = A
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => r1_xreal_0(k10_prepower(B,C),A) ) ) ) ),
    file(prepower,t79_prepower),
    [interesting(0.9),axiom,file(prepower,t79_prepower)]).

fof(e3_121__prepower,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & v1_prepower(A)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & v4_seq_2(A)
      & c3_121__prepower = k2_seq_2(A)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_xreal_0(k10_prepower(A,B),c3_121__prepower) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_121__prepower])],[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_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_prepower,rc1_seq_1,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_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_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,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_k10_prepower,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k1_numbers,dt_k2_seq_2,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c3_121__prepower,cc2_xreal_0,fc2_membered,t79_prepower]),
    [interesting(0.8),file(prepower,e3_121__prepower),[file(prepower,e3_121__prepower)]]).

fof(dt_c4_121__prepower,plain,
    ( v1_funct_1(c4_121__prepower)
    & v1_funct_2(c4_121__prepower,k5_numbers,k1_numbers)
    & v1_prepower(c4_121__prepower)
    & m2_relset_1(c4_121__prepower,k5_numbers,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c3_121__prepower])],[dh_c4_121__prepower,e3_121__prepower]),
    [interesting(0.8),file(prepower,c4_121__prepower),[file(prepower,c4_121__prepower)]]).

fof(fc1_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc1_xreal_0)]).

fof(fc4_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc4_xreal_0)]).

fof(fc5_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc5_xreal_0)]).

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__r0_rm1,theorem,(
    ~ r1_xreal_0(0,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1)]).

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(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(rqLessOrEqual__r1_xreal_0__r1_rm1,theorem,(
    ~ r1_xreal_0(1,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r0,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r1,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rm1,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,(
    k6_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,(
    k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,(
    k6_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,(
    k3_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,(
    k3_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]).

fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,(
    k3_xcmplx_0(1,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_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(dh_c1_121_1__prepower,definition,
    ( ( m2_subset_1(c1_121_1__prepower,k1_numbers,k5_numbers)
     => k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),c1_121_1__prepower) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),c1_121_1__prepower)) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),A) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),A)) ) ),
    introduced(definition,[new_symbol(c1_121_1__prepower),file(prepower,c1_121_1__prepower)]),
    [interesting(0.65),axiom,file(prepower,c1_121_1__prepower)]).

fof(fc3_prepower,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k8_prepower(A,B))
        & v1_xreal_0(k8_prepower(A,B)) ) ) ),
    file(prepower,fc3_prepower),
    [interesting(0.9),axiom,file(prepower,fc3_prepower)]).

fof(dt_k8_prepower,axiom,(
    $true ),
    file(prepower,k8_prepower),
    [interesting(0.9),axiom,file(prepower,k8_prepower)]).

fof(dt_c1_121_1__prepower,assumption,(
    m2_subset_1(c1_121_1__prepower,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(prepower,c1_121_1__prepower)]),
    [interesting(0.65),axiom,file(prepower,c1_121_1__prepower)]).

fof(fc2_prepower,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k6_prepower(A,B))
        & v1_xreal_0(k6_prepower(A,B)) ) ) ),
    file(prepower,fc2_prepower),
    [interesting(0.9),axiom,file(prepower,fc2_prepower)]).

fof(dt_k1_rat_1,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => m2_subset_1(k1_rat_1(A),k1_numbers,k5_numbers) ) ),
    file(rat_1,k1_rat_1),
    [interesting(0.9),axiom,file(rat_1,k1_rat_1)]).

fof(dt_k2_rat_1,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => v1_int_1(k2_rat_1(A)) ) ),
    file(rat_1,k2_rat_1),
    [interesting(0.9),axiom,file(rat_1,k2_rat_1)]).

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_k6_prepower,axiom,(
    $true ),
    file(prepower,k6_prepower),
    [interesting(0.9),axiom,file(prepower,k6_prepower)]).

fof(d5_prepower,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_rat_1(B)
         => k8_prepower(A,B) = k4_prepower(k1_rat_1(B),k6_prepower(A,k2_rat_1(B))) ) ) ),
    file(prepower,d5_prepower),
    [interesting(0.9),axiom,file(prepower,d5_prepower)]).

fof(d7_prepower,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v1_prepower(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( C = k11_prepower(A,B)
              <=> ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_seq_1(k5_numbers,k1_numbers,C,D) = k8_prepower(A,k10_prepower(B,D)) ) ) ) ) ) ),
    file(prepower,d7_prepower),
    [interesting(0.9),axiom,file(prepower,d7_prepower)]).

fof(e1_121_1_1__prepower,plain,(
    k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),c1_121_1__prepower) = k8_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),k10_prepower(c4_121__prepower,c1_121_1__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[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_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,fc2_prepower,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_rat_1,dt_k1_zfmisc_1,dt_k2_rat_1,dt_k2_zfmisc_1,dt_k4_prepower,dt_k5_ordinal2,dt_k6_prepower,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc3_prepower,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,existence_m2_subset_1,redefinition_k10_prepower,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k11_prepower,dt_k12_prepower,dt_k1_numbers,dt_k2_seq_1,dt_k5_numbers,dt_k8_prepower,dt_m2_relset_1,dt_m2_subset_1,dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc2_membered,d5_prepower,d7_prepower]),
    [interesting(0.5),file(prepower,e1_121_1_1__prepower),[file(prepower,e1_121_1_1__prepower)]]).

fof(l123_prepower,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_rat_1(C)
             => ( ~ r1_xreal_0(A,0)
               => k8_prepower(k12_prepower(A,B),C) = k12_prepower(A,k3_xcmplx_0(B,C)) ) ) ) ) ),
    file(prepower,l123_prepower),
    [interesting(0.9),axiom,file(prepower,l123_prepower)]).

fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,(
    k3_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]).

fof(e2_121_1_1__prepower,plain,(
    k8_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),k10_prepower(c4_121__prepower,c1_121_1__prepower)) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,k10_prepower(c4_121__prepower,c1_121_1__prepower))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c3_121__prepower,e1_121__prepower])],[reflexivity_r1_tarski,fc1_seq_1,rc1_prepower,rc1_seq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_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_relset_1,cc1_seq_1,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,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc2_nat_1,fc2_prepower,fc5_membered,fc6_membered,fc6_rat_1,fc7_int_1,fc9_rat_1,rc1_int_1,rc1_membered,rc1_nat_1,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_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_rat_1,dt_k2_rat_1,dt_k4_prepower,dt_k5_numbers,dt_k6_prepower,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_int_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_rat_1,fc15_rat_1,fc23_xreal_0,fc2_membered,rc1_rat_1,rc1_xreal_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k10_prepower,dt_k10_prepower,dt_k12_prepower,dt_k3_xcmplx_0,dt_k8_prepower,dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c4_121__prepower,cc1_rat_1,cc2_xreal_0,fc1_rat_1,fc3_prepower,fc4_xreal_0,rc2_rat_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,d5_prepower,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_121__prepower,l123_prepower,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(prepower,e2_121_1_1__prepower),[file(prepower,e2_121_1_1__prepower)]]).

fof(t13_seq_1,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) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( B = k14_seq_1(C,A)
              <=> ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_seq_1(k5_numbers,k1_numbers,B,D) = k3_xcmplx_0(A,k2_seq_1(k5_numbers,k1_numbers,C,D)) ) ) ) ) ) ),
    file(seq_1,t13_seq_1),
    [interesting(0.9),axiom,file(seq_1,t13_seq_1)]).

fof(e3_121_1_1__prepower,plain,(
    k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,k10_prepower(c4_121__prepower,c1_121_1__prepower))) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),c1_121_1__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[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,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_seq_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc2_nat_1,fc6_membered,fc6_rat_1,fc6_seq_1,fc7_int_1,fc9_rat_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_k12_seq_1,dt_k1_funct_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_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc12_rat_1,fc15_rat_1,fc1_ordinal2,fc1_rat_1,fc23_xreal_0,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,spc7_arithm,t2_subset,t3_arithm,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k10_prepower,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k12_prepower,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc2_membered,fc4_xreal_0,spc1_numerals,spc1_boole,t13_seq_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(prepower,e3_121_1_1__prepower),[file(prepower,e3_121_1_1__prepower)]]).

fof(e1_121_1__prepower,plain,(
    k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),c1_121_1__prepower) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),c1_121_1__prepower)) ),
    inference(iterative_eq,[status(thm),assumptions([e1_121__prepower,dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[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,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc2_int_1,fc2_nat_1,fc6_rat_1,fc6_seq_1,fc7_int_1,fc9_rat_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,rc2_int_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc1_rat_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc12_rat_1,fc15_rat_1,fc1_ordinal2,fc1_rat_1,fc3_prepower,fc4_xreal_0,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,commutativity_k3_xcmplx_0,redefinition_k10_prepower,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k5_numbers,dt_k10_prepower,dt_k11_prepower,dt_k12_prepower,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k5_numbers,dt_k8_prepower,dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c4_121__prepower,fc2_membered,e1_121_1_1__prepower,e2_121_1_1__prepower,e3_121_1_1__prepower]),
    [interesting(0.65),file(prepower,e1_121_1__prepower),[file(prepower,e1_121_1__prepower)]]).

fof(i2_121_1__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i2_121_1__prepower)]),
    [interesting(0.65),trivial,file(prepower,i2_121_1__prepower)]).

fof(i1_121_1__prepower,plain,(
    k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),c1_121_1__prepower) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),c1_121_1__prepower)) ),
    inference(conclusion,[status(thm),assumptions([e1_121__prepower,dt_c1_121__prepower,dt_c1_121_1__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[e1_121_1__prepower,i2_121_1__prepower]),
    [interesting(0.65),file(prepower,i1_121_1__prepower),[file(prepower,i1_121_1__prepower)]]).

fof(i1_121_1_tmp__prepower,plain,
    ( m2_subset_1(c1_121_1__prepower,k1_numbers,k5_numbers)
   => k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),c1_121_1__prepower) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),c1_121_1__prepower)) ),
    inference(discharge_asm,[status(thm),assumptions([e1_121__prepower,dt_c1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower]),discharge_asm(discharge,[dt_c1_121_1__prepower])],[dt_c1_121_1__prepower,i1_121_1__prepower]),
    [interesting(0.8),e9_121__prepower]).

fof(e9_121__prepower,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_seq_1(k5_numbers,k1_numbers,k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower),A) = k12_prepower(c1_121__prepower,k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_121__prepower,c2_121__prepower),A)) ) ),
    inference(let,[status(thm),assumptions([e1_121__prepower,dt_c1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[i1_121_1_tmp__prepower,dh_c1_121_1__prepower]),
    [interesting(0.8),file(prepower,e9_121__prepower),[file(prepower,e9_121__prepower)]]).

fof(t95_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k12_prepower(A,B),0) ) ) ) ),
    file(prepower,t95_prepower),
    [interesting(0.9),axiom,file(prepower,t95_prepower)]).

fof(e2_121__prepower,plain,(
    ~ r1_xreal_0(k12_prepower(c1_121__prepower,c2_121__prepower),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,dt_c2_121__prepower,e1_121__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,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_boole,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,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k12_prepower,dt_c1_121__prepower,dt_c2_121__prepower,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e1_121__prepower,t95_prepower]),
    [interesting(0.8),file(prepower,e2_121__prepower),[file(prepower,e2_121__prepower)]]).

fof(e4_121__prepower,plain,
    ( v4_seq_2(c4_121__prepower)
    & c3_121__prepower = k2_seq_2(c4_121__prepower)
    & ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => r1_xreal_0(k10_prepower(c4_121__prepower,A),c3_121__prepower) ) ),
    inference(consider,[status(thm),assumptions([dt_c3_121__prepower])],[dh_c4_121__prepower,e3_121__prepower]),
    [interesting(0.8),file(prepower,e4_121__prepower),[file(prepower,e4_121__prepower)]]).

fof(t82_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & v1_prepower(B)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v4_seq_2(B)
           => ( r1_xreal_0(A,0)
              | v4_seq_2(k11_prepower(A,B)) ) ) ) ) ),
    file(prepower,t82_prepower),
    [interesting(0.9),axiom,file(prepower,t82_prepower)]).

fof(e5_121__prepower,plain,(
    v4_seq_2(k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,dt_c2_121__prepower,e1_121__prepower,dt_c3_121__prepower])],[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,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_seq_1,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_seq_2,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_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,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_relset_1,existence_m2_subset_1,redefinition_k10_prepower,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k11_prepower,dt_k12_prepower,dt_k1_numbers,dt_k2_seq_2,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e2_121__prepower,e4_121__prepower,t82_prepower]),
    [interesting(0.8),file(prepower,e5_121__prepower),[file(prepower,e5_121__prepower)]]).

fof(d8_prepower,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(A,0)
           => ! [C] : 
                ( v1_xreal_0(C)
               => ( C = k12_prepower(A,B)
                <=> ? [D] : 
                      ( v1_funct_1(D)
                      & v1_funct_2(D,k5_numbers,k1_numbers)
                      & v1_prepower(D)
                      & m2_relset_1(D,k5_numbers,k1_numbers)
                      & v4_seq_2(D)
                      & k2_seq_2(D) = B
                      & v4_seq_2(k11_prepower(A,D))
                      & k2_seq_2(k11_prepower(A,D)) = C ) ) ) ) ) ) ),
    file(prepower,d8_prepower),
    [interesting(0.9),axiom,file(prepower,d8_prepower)]).

fof(e6_121__prepower,plain,(
    k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c3_121__prepower) = k2_seq_2(k11_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c4_121__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,dt_c2_121__prepower,e1_121__prepower,dt_c3_121__prepower])],[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,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_seq_1,fc6_membered,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_seq_2,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_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,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_relset_1,existence_m2_subset_1,redefinition_k10_prepower,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k11_prepower,dt_k12_prepower,dt_k1_numbers,dt_k2_seq_2,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e5_121__prepower,e2_121__prepower,e4_121__prepower,d8_prepower]),
    [interesting(0.8),file(prepower,e6_121__prepower),[file(prepower,e6_121__prepower)]]).

fof(t21_seq_2,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)
           => v4_seq_2(k14_seq_1(B,A)) ) ) ) ),
    file(seq_2,t21_seq_2),
    [interesting(0.9),axiom,file(seq_2,t21_seq_2)]).

fof(e7_121__prepower,plain,(
    v4_seq_2(k14_seq_1(c4_121__prepower,c2_121__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_121__prepower,dt_c3_121__prepower])],[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_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_seq_1,fc6_membered,fc6_seq_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,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_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,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_k10_prepower,redefinition_k14_seq_1,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_2,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c2_121__prepower,dt_c3_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc2_membered,e4_121__prepower,t21_seq_2]),
    [interesting(0.8),file(prepower,e7_121__prepower),[file(prepower,e7_121__prepower)]]).

fof(t22_seq_2,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)
           => k2_seq_2(k14_seq_1(B,A)) = k3_xcmplx_0(A,k2_seq_2(B)) ) ) ) ),
    file(seq_2,t22_seq_2),
    [interesting(0.9),axiom,file(seq_2,t22_seq_2)]).

fof(e8_121__prepower,plain,(
    k2_seq_2(k14_seq_1(c4_121__prepower,c2_121__prepower)) = k3_xcmplx_0(c2_121__prepower,c3_121__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_121__prepower,dt_c3_121__prepower])],[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,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_seq_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc2_nat_1,fc6_membered,fc6_rat_1,fc6_seq_1,fc7_int_1,fc9_rat_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_relset_1,existence_m1_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,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_rat_1,cc1_relset_1,cc1_seq_1,cc2_int_1,cc2_nat_1,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc12_rat_1,fc15_rat_1,fc1_ordinal2,fc1_rat_1,fc23_xreal_0,fc5_membered,rc1_rat_1,rc1_xreal_0,rc2_rat_1,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k10_prepower,redefinition_k14_seq_1,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_prepower,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_2,dt_k3_xcmplx_0,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_c2_121__prepower,dt_c3_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc2_membered,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e4_121__prepower,t22_seq_2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.8),file(prepower,e8_121__prepower),[file(prepower,e8_121__prepower)]]).

fof(t104_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) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( ( v4_seq_2(B)
                  & v4_seq_2(C)
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k2_seq_1(k5_numbers,k1_numbers,C,D) = k12_prepower(A,k2_seq_1(k5_numbers,k1_numbers,B,D)) ) )
               => ( r1_xreal_0(A,0)
                  | k2_seq_2(C) = k12_prepower(A,k2_seq_2(B)) ) ) ) ) ) ),
    file(prepower,t104_prepower),
    [interesting(0.9),axiom,file(prepower,t104_prepower)]).

fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,(
    k4_xcmplx_0(1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]).

fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,(
    k4_xcmplx_0(0) = 0 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,(
    k6_xcmplx_0(1,1) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]).

fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]).

fof(e10_121__prepower,plain,(
    k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c3_121__prepower) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,c3_121__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_121__prepower,e1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[cc1_rat_1,fc11_rat_1,fc12_rat_1,fc14_rat_1,fc15_rat_1,fc16_rat_1,fc1_rat_1,fc3_rat_1,fc5_rat_1,fc6_rat_1,fc8_rat_1,fc9_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,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_seq_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_int_1,fc2_nat_1,fc3_int_1,fc4_int_1,fc6_membered,fc6_seq_1,fc7_int_1,fc8_int_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_prepower,rc1_seq_1,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_relset_1,existence_m1_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,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,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc23_xreal_0,fc5_int_1,fc5_membered,fc9_int_1,rc1_xreal_0,spc2_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k11_prepower,dt_k12_prepower,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_1,dt_k2_seq_2,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_xcmplx_0,dt_m2_relset_1,dt_m2_subset_1,dt_c1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower,dt_c4_121__prepower,cc2_xreal_0,fc1_xreal_0,fc2_membered,fc4_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_121__prepower,e1_121__prepower,e5_121__prepower,e6_121__prepower,e7_121__prepower,e8_121__prepower,t104_prepower,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1]),
    [interesting(0.8),file(prepower,e10_121__prepower),[file(prepower,e10_121__prepower)]]).

fof(i5_121__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i5_121__prepower)]),
    [interesting(0.8),trivial,file(prepower,i5_121__prepower)]).

fof(i4_121__prepower,plain,(
    k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c3_121__prepower) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,c3_121__prepower)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_121__prepower,e1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower])],[e10_121__prepower,i5_121__prepower]),
    [interesting(0.8),file(prepower,i4_121__prepower),[file(prepower,i4_121__prepower)]]).

fof(i3_121__prepower,plain,
    ( ~ r1_xreal_0(c1_121__prepower,0)
   => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c3_121__prepower) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,c3_121__prepower)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_121__prepower,dt_c2_121__prepower,dt_c3_121__prepower]),discharge_asm(discharge,[e1_121__prepower])],[e1_121__prepower,i4_121__prepower]),
    [interesting(0.8),file(prepower,i3_121__prepower),[file(prepower,i3_121__prepower)]]).

fof(i3_121_tmp__prepower,plain,
    ( v1_xreal_0(c3_121__prepower)
   => ( ~ r1_xreal_0(c1_121__prepower,0)
     => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),c3_121__prepower) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,c3_121__prepower)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_121__prepower,dt_c2_121__prepower]),discharge_asm(discharge,[dt_c3_121__prepower])],[dt_c3_121__prepower,i3_121__prepower]),
    [interesting(0.8),i2_121__prepower]).

fof(i2_121__prepower,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(c1_121__prepower,0)
       => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),A) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_121__prepower,dt_c2_121__prepower])],[i3_121_tmp__prepower,dh_c3_121__prepower]),
    [interesting(0.8),file(prepower,i2_121__prepower),[file(prepower,i2_121__prepower)]]).

fof(i2_121_tmp__prepower,plain,
    ( v1_xreal_0(c2_121__prepower)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ~ r1_xreal_0(c1_121__prepower,0)
         => k12_prepower(k12_prepower(c1_121__prepower,c2_121__prepower),A) = k12_prepower(c1_121__prepower,k3_xcmplx_0(c2_121__prepower,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_121__prepower]),discharge_asm(discharge,[dt_c2_121__prepower])],[dt_c2_121__prepower,i2_121__prepower]),
    [interesting(0.8),i1_121__prepower]).

fof(i1_121__prepower,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(c1_121__prepower,0)
           => k12_prepower(k12_prepower(c1_121__prepower,A),B) = k12_prepower(c1_121__prepower,k3_xcmplx_0(A,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_121__prepower])],[i2_121_tmp__prepower,dh_c2_121__prepower]),
    [interesting(0.8),file(prepower,i1_121__prepower),[file(prepower,i1_121__prepower)]]).

fof(i1_121_tmp__prepower,plain,
    ( v1_xreal_0(c1_121__prepower)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ! [B] : 
            ( v1_xreal_0(B)
           => ( ~ r1_xreal_0(c1_121__prepower,0)
             => k12_prepower(k12_prepower(c1_121__prepower,A),B) = k12_prepower(c1_121__prepower,k3_xcmplx_0(A,B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_121__prepower])],[dt_c1_121__prepower,i1_121__prepower]),
    [interesting(1),t105_prepower]).

fof(t105_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(A,0)
               => k12_prepower(k12_prepower(A,B),C) = k12_prepower(A,k3_xcmplx_0(B,C)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_121_tmp__prepower,dh_c1_121__prepower]),
    [interesting(1),file(prepower,t105_prepower),[file(prepower,t105_prepower)]]).