% Mizar ND problem: t69_prepower,prepower,1563,50 
fof(dh_c1_74__prepower,definition,
    ( ( v1_xreal_0(c1_74__prepower)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ! [B] : 
              ( v1_rat_1(B)
             => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
                  & ~ r1_xreal_0(A,0)
                  & k8_prepower(k7_xcmplx_0(c1_74__prepower,A),B) != k7_xcmplx_0(k8_prepower(c1_74__prepower,B),k8_prepower(A,B)) ) ) ) )
   => ! [C] : 
        ( v1_xreal_0(C)
       => ! [D] : 
            ( v1_xreal_0(D)
           => ! [E] : 
                ( v1_rat_1(E)
               => ~ ( ~ r1_xreal_0(C,0)
                    & ~ r1_xreal_0(D,0)
                    & k8_prepower(k7_xcmplx_0(C,D),E) != k7_xcmplx_0(k8_prepower(C,E),k8_prepower(D,E)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_74__prepower),file(prepower,c1_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_74__prepower)]).

fof(dh_c2_74__prepower,definition,
    ( ( v1_xreal_0(c2_74__prepower)
     => ! [A] : 
          ( v1_rat_1(A)
         => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
              & ~ r1_xreal_0(c2_74__prepower,0)
              & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),A) != k7_xcmplx_0(k8_prepower(c1_74__prepower,A),k8_prepower(c2_74__prepower,A)) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( v1_rat_1(C)
           => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
                & ~ r1_xreal_0(B,0)
                & k8_prepower(k7_xcmplx_0(c1_74__prepower,B),C) != k7_xcmplx_0(k8_prepower(c1_74__prepower,C),k8_prepower(B,C)) ) ) ) ),
    introduced(definition,[new_symbol(c2_74__prepower),file(prepower,c2_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_74__prepower)]).

fof(dh_c3_74__prepower,definition,
    ( ( v1_rat_1(c3_74__prepower)
     => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
          & ~ r1_xreal_0(c2_74__prepower,0)
          & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),c3_74__prepower) != k7_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(c2_74__prepower,c3_74__prepower)) ) )
   => ! [A] : 
        ( v1_rat_1(A)
       => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
            & ~ r1_xreal_0(c2_74__prepower,0)
            & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),A) != k7_xcmplx_0(k8_prepower(c1_74__prepower,A),k8_prepower(c2_74__prepower,A)) ) ) ),
    introduced(definition,[new_symbol(c3_74__prepower),file(prepower,c3_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,c3_74__prepower)]).

fof(e1_74__prepower,assumption,
    ( ~ r1_xreal_0(c1_74__prepower,0)
    & ~ r1_xreal_0(c2_74__prepower,0) ),
    introduced(assumption,[file(prepower,e1_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,e1_74__prepower)]).

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

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_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(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(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(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(fc27_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc27_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc27_xreal_0)]).

fof(fc28_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(B,A))
        & v1_xreal_0(k7_xcmplx_0(B,A))
        & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc28_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc28_xreal_0)]).

fof(fc29_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc29_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc29_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(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(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(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_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(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(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_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(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(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_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(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(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_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_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_prepower,axiom,(
    $true ),
    file(prepower,k6_prepower),
    [interesting(0.9),axiom,file(prepower,k6_prepower)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_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(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(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_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(cc2_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    [interesting(0.9),axiom,file(int_1,cc2_int_1)]).

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

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(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(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(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(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(fc17_rat_1,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & v1_rat_1(k7_xcmplx_0(A,B)) ) ) ),
    file(rat_1,fc17_rat_1),
    [interesting(0.9),axiom,file(rat_1,fc17_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(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(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(fc30_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc30_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc30_xreal_0)]).

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(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(fc6_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]).

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

fof(rc2_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(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

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

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

fof(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(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]).

fof(dt_k7_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k7_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]).

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

fof(dt_c1_74__prepower,assumption,(
    v1_xreal_0(c1_74__prepower) ),
    introduced(assumption,[file(prepower,c1_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,c1_74__prepower)]).

fof(dt_c2_74__prepower,assumption,(
    v1_xreal_0(c2_74__prepower) ),
    introduced(assumption,[file(prepower,c2_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,c2_74__prepower)]).

fof(dt_c3_74__prepower,assumption,(
    v1_rat_1(c3_74__prepower) ),
    introduced(assumption,[file(prepower,c3_74__prepower)]),
    [interesting(0.8),axiom,file(prepower,c3_74__prepower)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,(
    k7_xcmplx_0(1,1) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]).

fof(spc4_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ),
    file(arithm,spc4_arithm),
    [interesting(0.9),axiom,file(arithm,spc4_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(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(t6_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,1) = A ) ),
    file(arithm,t6_arithm),
    [interesting(0.9),axiom,file(arithm,t6_arithm)]).

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

fof(t100_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(A,k7_xcmplx_0(1,B)) = k7_xcmplx_0(A,B) ) ) ),
    file(xcmplx_1,t100_xcmplx_1),
    [interesting(0.9),axiom,file(xcmplx_1,t100_xcmplx_1)]).

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(e1_74_1__prepower,plain,(
    k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),c3_74__prepower) = k8_prepower(k3_xcmplx_0(c1_74__prepower,k7_xcmplx_0(1,c2_74__prepower)),c3_74__prepower) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__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_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,fc27_xreal_0,fc28_xreal_0,fc29_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,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_k1_rat_1,dt_k2_rat_1,dt_k4_prepower,dt_k5_numbers,dt_k6_prepower,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc1_rat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_rat_1,fc15_rat_1,fc17_rat_1,fc1_rat_1,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc3_prepower,fc4_xreal_0,fc6_xreal_0,rc1_rat_1,rc1_xreal_0,rc2_rat_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,dt_k3_xcmplx_0,dt_k7_xcmplx_0,dt_k8_prepower,dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower,rqRealDiv__k7_xcmplx_0__r1_r1_r1,spc4_arithm,spc7_arithm,t3_arithm,t6_arithm,d5_prepower,spc1_numerals,spc1_boole,t100_xcmplx_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.65),file(prepower,e1_74_1__prepower),[file(prepower,e1_74_1__prepower)]]).

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(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(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(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(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(t5_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(0,A) = 0 ) ),
    file(arithm,t5_arithm),
    [interesting(0.9),axiom,file(arithm,t5_arithm)]).

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(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(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,(
    k7_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_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(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(t127_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(B,0) )
                | ( ~ r1_xreal_0(0,A)
                  & ~ r1_xreal_0(0,B) ) )
              & r1_xreal_0(k7_xcmplx_0(A,B),0) ) ) ) ),
    file(real_2,t127_real_2),
    [interesting(0.9),axiom,file(real_2,t127_real_2)]).

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(e2_74__prepower,plain,(
    ~ r1_xreal_0(k7_xcmplx_0(1,c2_74__prepower),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower,e1_74__prepower])],[reflexivity_r1_tarski,cc1_rat_1,fc17_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,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,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,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_arithm,t5_real,t5_subset,t6_arithm,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,fc30_xreal_0,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k7_xcmplx_0,dt_c1_74__prepower,dt_c2_74__prepower,cc2_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_74__prepower,t127_real_2,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.8),file(prepower,e2_74__prepower),[file(prepower,e2_74__prepower)]]).

fof(t67_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_rat_1(C)
             => ~ ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(B,0)
                  & k8_prepower(k3_xcmplx_0(A,B),C) != k3_xcmplx_0(k8_prepower(A,C),k8_prepower(B,C)) ) ) ) ) ),
    file(prepower,t67_prepower),
    [interesting(0.9),axiom,file(prepower,t67_prepower)]).

fof(e2_74_1__prepower,plain,(
    k8_prepower(k3_xcmplx_0(c1_74__prepower,k7_xcmplx_0(1,c2_74__prepower)),c3_74__prepower) = k3_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(k7_xcmplx_0(1,c2_74__prepower),c3_74__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_74__prepower,dt_c1_74__prepower,dt_c2_74__prepower,e1_74__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_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,fc27_xreal_0,fc28_xreal_0,fc29_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_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_rat_1,dt_k2_rat_1,dt_k4_prepower,dt_k5_numbers,dt_k6_prepower,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,fc12_rat_1,fc15_rat_1,fc23_xreal_0,fc2_membered,fc30_xreal_0,rc1_rat_1,rc1_xreal_0,spc4_arithm,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k3_xcmplx_0,dt_k7_xcmplx_0,dt_k8_prepower,dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower,cc1_rat_1,cc2_xreal_0,fc17_rat_1,fc1_rat_1,fc3_prepower,fc4_xreal_0,fc6_xreal_0,rc2_rat_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_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_74__prepower,e2_74__prepower,t67_prepower,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.65),file(prepower,e2_74_1__prepower),[file(prepower,e2_74_1__prepower)]]).

fof(t68_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_rat_1(B)
         => ( ~ r1_xreal_0(A,0)
           => k8_prepower(k7_xcmplx_0(1,A),B) = k7_xcmplx_0(1,k8_prepower(A,B)) ) ) ) ),
    file(prepower,t68_prepower),
    [interesting(0.9),axiom,file(prepower,t68_prepower)]).

fof(e3_74_1__prepower,plain,(
    k3_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(k7_xcmplx_0(1,c2_74__prepower),c3_74__prepower)) = k3_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k7_xcmplx_0(1,k8_prepower(c2_74__prepower,c3_74__prepower))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower,e1_74__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_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,fc27_xreal_0,fc28_xreal_0,fc29_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_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_rat_1,dt_k2_rat_1,dt_k4_prepower,dt_k5_numbers,dt_k6_prepower,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,fc12_rat_1,fc15_rat_1,fc23_xreal_0,fc2_membered,fc30_xreal_0,rc1_rat_1,rc1_xreal_0,spc4_arithm,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k3_xcmplx_0,dt_k7_xcmplx_0,dt_k8_prepower,dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower,cc1_rat_1,cc2_xreal_0,fc17_rat_1,fc1_rat_1,fc3_prepower,fc4_xreal_0,fc6_xreal_0,rc2_rat_1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_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_74__prepower,t68_prepower,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.65),file(prepower,e3_74_1__prepower),[file(prepower,e3_74_1__prepower)]]).

fof(e4_74_1__prepower,plain,(
    k3_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k7_xcmplx_0(1,k8_prepower(c2_74__prepower,c3_74__prepower))) = k7_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(c2_74__prepower,c3_74__prepower)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__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_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,fc27_xreal_0,fc28_xreal_0,fc29_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,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_k1_rat_1,dt_k2_rat_1,dt_k4_prepower,dt_k5_numbers,dt_k6_prepower,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc1_rat_1,cc2_int_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_rat_1,fc15_rat_1,fc17_rat_1,fc1_rat_1,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc3_prepower,fc4_xreal_0,fc6_xreal_0,rc1_rat_1,rc1_xreal_0,rc2_rat_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,dt_k3_xcmplx_0,dt_k7_xcmplx_0,dt_k8_prepower,dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower,rqRealDiv__k7_xcmplx_0__r1_r1_r1,spc4_arithm,spc7_arithm,t3_arithm,t6_arithm,d5_prepower,spc1_numerals,spc1_boole,t100_xcmplx_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.65),file(prepower,e4_74_1__prepower),[file(prepower,e4_74_1__prepower)]]).

fof(e3_74__prepower,plain,(
    k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),c3_74__prepower) = k7_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(c2_74__prepower,c3_74__prepower)) ),
    inference(iterative_eq,[status(thm),assumptions([e1_74__prepower,dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower])],[e1_74_1__prepower,e2_74_1__prepower,e3_74_1__prepower,e4_74_1__prepower]),
    [interesting(0.8),file(prepower,e3_74__prepower),[file(prepower,e3_74__prepower)]]).

fof(i5_74__prepower,theorem,(
    $true ),
    introduced(tautology,[file(prepower,i5_74__prepower)]),
    [interesting(0.8),trivial,file(prepower,i5_74__prepower)]).

fof(i4_74__prepower,plain,(
    k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),c3_74__prepower) = k7_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(c2_74__prepower,c3_74__prepower)) ),
    inference(conclusion,[status(thm),assumptions([e1_74__prepower,dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower])],[e3_74__prepower,i5_74__prepower]),
    [interesting(0.8),file(prepower,i4_74__prepower),[file(prepower,i4_74__prepower)]]).

fof(i3_74__prepower,plain,(
    ~ ( ~ r1_xreal_0(c1_74__prepower,0)
      & ~ r1_xreal_0(c2_74__prepower,0)
      & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),c3_74__prepower) != k7_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(c2_74__prepower,c3_74__prepower)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower,dt_c3_74__prepower]),discharge_asm(discharge,[e1_74__prepower])],[e1_74__prepower,i4_74__prepower]),
    [interesting(0.8),file(prepower,i3_74__prepower),[file(prepower,i3_74__prepower)]]).

fof(i3_74_tmp__prepower,plain,
    ( v1_rat_1(c3_74__prepower)
   => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
        & ~ r1_xreal_0(c2_74__prepower,0)
        & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),c3_74__prepower) != k7_xcmplx_0(k8_prepower(c1_74__prepower,c3_74__prepower),k8_prepower(c2_74__prepower,c3_74__prepower)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower]),discharge_asm(discharge,[dt_c3_74__prepower])],[dt_c3_74__prepower,i3_74__prepower]),
    [interesting(0.8),i2_74__prepower]).

fof(i2_74__prepower,plain,(
    ! [A] : 
      ( v1_rat_1(A)
     => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
          & ~ r1_xreal_0(c2_74__prepower,0)
          & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),A) != k7_xcmplx_0(k8_prepower(c1_74__prepower,A),k8_prepower(c2_74__prepower,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_74__prepower,dt_c2_74__prepower])],[i3_74_tmp__prepower,dh_c3_74__prepower]),
    [interesting(0.8),file(prepower,i2_74__prepower),[file(prepower,i2_74__prepower)]]).

fof(i2_74_tmp__prepower,plain,
    ( v1_xreal_0(c2_74__prepower)
   => ! [A] : 
        ( v1_rat_1(A)
       => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
            & ~ r1_xreal_0(c2_74__prepower,0)
            & k8_prepower(k7_xcmplx_0(c1_74__prepower,c2_74__prepower),A) != k7_xcmplx_0(k8_prepower(c1_74__prepower,A),k8_prepower(c2_74__prepower,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_74__prepower]),discharge_asm(discharge,[dt_c2_74__prepower])],[dt_c2_74__prepower,i2_74__prepower]),
    [interesting(0.8),i1_74__prepower]).

fof(i1_74__prepower,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_rat_1(B)
         => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
              & ~ r1_xreal_0(A,0)
              & k8_prepower(k7_xcmplx_0(c1_74__prepower,A),B) != k7_xcmplx_0(k8_prepower(c1_74__prepower,B),k8_prepower(A,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_74__prepower])],[i2_74_tmp__prepower,dh_c2_74__prepower]),
    [interesting(0.8),file(prepower,i1_74__prepower),[file(prepower,i1_74__prepower)]]).

fof(i1_74_tmp__prepower,plain,
    ( v1_xreal_0(c1_74__prepower)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ! [B] : 
            ( v1_rat_1(B)
           => ~ ( ~ r1_xreal_0(c1_74__prepower,0)
                & ~ r1_xreal_0(A,0)
                & k8_prepower(k7_xcmplx_0(c1_74__prepower,A),B) != k7_xcmplx_0(k8_prepower(c1_74__prepower,B),k8_prepower(A,B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_74__prepower])],[dt_c1_74__prepower,i1_74__prepower]),
    [interesting(1),t69_prepower]).

fof(t69_prepower,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_rat_1(C)
             => ~ ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(B,0)
                  & k8_prepower(k7_xcmplx_0(A,B),C) != k7_xcmplx_0(k8_prepower(A,C),k8_prepower(B,C)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_74_tmp__prepower,dh_c1_74__prepower]),
    [interesting(1),file(prepower,t69_prepower),[file(prepower,t69_prepower)]]).