% Mizar ND problem: t13_int_2,int_2,200,51 
fof(dh_c1_10__int_2,definition,
    ( ( v1_int_1(c1_10__int_2)
     => ! [A] : 
          ( v1_int_1(A)
         => ! [B] : 
              ( v1_int_1(B)
             => ( ( r2_int_1(c1_10__int_2,A)
                  & r2_int_1(A,B) )
               => r2_int_1(c1_10__int_2,B) ) ) ) )
   => ! [C] : 
        ( v1_int_1(C)
       => ! [D] : 
            ( v1_int_1(D)
           => ! [E] : 
                ( v1_int_1(E)
               => ( ( r2_int_1(C,D)
                    & r2_int_1(D,E) )
                 => r2_int_1(C,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_10__int_2),file(int_2,c1_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c1_10__int_2)]).

fof(dh_c2_10__int_2,definition,
    ( ( v1_int_1(c2_10__int_2)
     => ! [A] : 
          ( v1_int_1(A)
         => ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
              & r2_int_1(c2_10__int_2,A) )
           => r2_int_1(c1_10__int_2,A) ) ) )
   => ! [B] : 
        ( v1_int_1(B)
       => ! [C] : 
            ( v1_int_1(C)
           => ( ( r2_int_1(c1_10__int_2,B)
                & r2_int_1(B,C) )
             => r2_int_1(c1_10__int_2,C) ) ) ) ),
    introduced(definition,[new_symbol(c2_10__int_2),file(int_2,c2_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c2_10__int_2)]).

fof(dh_c3_10__int_2,definition,
    ( ( v1_int_1(c3_10__int_2)
     => ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
          & r2_int_1(c2_10__int_2,c3_10__int_2) )
       => r2_int_1(c1_10__int_2,c3_10__int_2) ) )
   => ! [A] : 
        ( v1_int_1(A)
       => ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
            & r2_int_1(c2_10__int_2,A) )
         => r2_int_1(c1_10__int_2,A) ) ) ),
    introduced(definition,[new_symbol(c3_10__int_2),file(int_2,c3_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c3_10__int_2)]).

fof(e1_10__int_2,assumption,(
    r2_int_1(c1_10__int_2,c2_10__int_2) ),
    introduced(assumption,[file(int_2,e1_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,e1_10__int_2)]).

fof(e2_10__int_2,assumption,(
    r2_int_1(c2_10__int_2,c3_10__int_2) ),
    introduced(assumption,[file(int_2,e2_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,e2_10__int_2)]).

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(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

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

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

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

fof(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_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_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(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(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(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(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(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(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(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_r2_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => r2_int_1(A,A) ) ),
    file(int_1,r2_int_1),
    [interesting(0.9),axiom,file(int_1,r2_int_1)]).

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_c1_10__int_2,assumption,(
    v1_int_1(c1_10__int_2) ),
    introduced(assumption,[file(int_2,c1_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c1_10__int_2)]).

fof(dt_c3_10__int_2,assumption,(
    v1_int_1(c3_10__int_2) ),
    introduced(assumption,[file(int_2,c3_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c3_10__int_2)]).

fof(dh_c4_10__int_2,definition,
    ( ? [A] : 
        ( v1_int_1(A)
        & c2_10__int_2 = k3_xcmplx_0(c1_10__int_2,A) )
   => ( v1_int_1(c4_10__int_2)
      & c2_10__int_2 = k3_xcmplx_0(c1_10__int_2,c4_10__int_2) ) ),
    introduced(definition,[new_symbol(c4_10__int_2),file(int_2,c4_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c4_10__int_2)]).

fof(dt_c2_10__int_2,assumption,(
    v1_int_1(c2_10__int_2) ),
    introduced(assumption,[file(int_2,c2_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c2_10__int_2)]).

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(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(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(d9_int_1,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r2_int_1(A,B)
          <=> ? [C] : 
                ( v1_int_1(C)
                & B = k3_xcmplx_0(A,C) ) ) ) ) ),
    file(int_1,d9_int_1),
    [interesting(0.9),axiom,file(int_1,d9_int_1)]).

fof(e3_10__int_2,plain,(
    ? [A] : 
      ( v1_int_1(A)
      & c2_10__int_2 = k3_xcmplx_0(c1_10__int_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__int_2,dt_c2_10__int_2,e1_10__int_2])],[spc7_arithm,commutativity_k3_xcmplx_0,reflexivity_r2_int_1,dt_k3_xcmplx_0,dt_c1_10__int_2,dt_c2_10__int_2,cc4_int_1,fc2_int_1,rc2_int_1,e1_10__int_2,d9_int_1]),
    [interesting(0.8),file(int_2,e3_10__int_2),[file(int_2,e3_10__int_2)]]).

fof(dt_c4_10__int_2,plain,(
    v1_int_1(c4_10__int_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_10__int_2,dt_c2_10__int_2,e1_10__int_2])],[dh_c4_10__int_2,e3_10__int_2]),
    [interesting(0.8),file(int_2,c4_10__int_2),[file(int_2,c4_10__int_2)]]).

fof(dh_c5_10__int_2,definition,
    ( ? [A] : 
        ( v1_int_1(A)
        & c3_10__int_2 = k3_xcmplx_0(c2_10__int_2,A) )
   => ( v1_int_1(c5_10__int_2)
      & c3_10__int_2 = k3_xcmplx_0(c2_10__int_2,c5_10__int_2) ) ),
    introduced(definition,[new_symbol(c5_10__int_2),file(int_2,c5_10__int_2)]),
    [interesting(0.8),axiom,file(int_2,c5_10__int_2)]).

fof(e5_10__int_2,plain,(
    ? [A] : 
      ( v1_int_1(A)
      & c3_10__int_2 = k3_xcmplx_0(c2_10__int_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_10__int_2,dt_c3_10__int_2,e2_10__int_2])],[spc7_arithm,commutativity_k3_xcmplx_0,reflexivity_r2_int_1,dt_k3_xcmplx_0,dt_c2_10__int_2,dt_c3_10__int_2,cc4_int_1,fc2_int_1,rc2_int_1,e2_10__int_2,d9_int_1]),
    [interesting(0.8),file(int_2,e5_10__int_2),[file(int_2,e5_10__int_2)]]).

fof(dt_c5_10__int_2,plain,(
    v1_int_1(c5_10__int_2) ),
    inference(consider,[status(thm),assumptions([dt_c2_10__int_2,dt_c3_10__int_2,e2_10__int_2])],[dh_c5_10__int_2,e5_10__int_2]),
    [interesting(0.8),file(int_2,c5_10__int_2),[file(int_2,c5_10__int_2)]]).

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(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(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(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(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(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(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(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(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_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(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(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(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k6_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(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__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(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(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(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(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,(
    k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]).

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(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(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(e4_10__int_2,plain,(
    c2_10__int_2 = k3_xcmplx_0(c1_10__int_2,c4_10__int_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_10__int_2,dt_c2_10__int_2,e1_10__int_2])],[dh_c4_10__int_2,e3_10__int_2]),
    [interesting(0.8),file(int_2,e4_10__int_2),[file(int_2,e4_10__int_2)]]).

fof(e6_10__int_2,plain,(
    c3_10__int_2 = k3_xcmplx_0(c2_10__int_2,c5_10__int_2) ),
    inference(consider,[status(thm),assumptions([dt_c2_10__int_2,dt_c3_10__int_2,e2_10__int_2])],[dh_c5_10__int_2,e5_10__int_2]),
    [interesting(0.8),file(int_2,e6_10__int_2),[file(int_2,e6_10__int_2)]]).

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(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(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_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(e7_10__int_2,plain,(
    c3_10__int_2 = k3_xcmplx_0(c1_10__int_2,k3_xcmplx_0(c4_10__int_2,c5_10__int_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__int_2,e1_10__int_2,dt_c2_10__int_2,dt_c3_10__int_2,e2_10__int_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_int_1,rc1_int_1,t2_subset,t3_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,cc4_int_1,fc2_int_1,fc3_int_1,fc4_int_1,fc5_int_1,fc7_int_1,fc8_int_1,fc9_int_1,rc2_int_1,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t2_arithm,t3_arithm,t4_arithm,t5_arithm,t6_arithm,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_10__int_2,dt_c2_10__int_2,dt_c3_10__int_2,dt_c4_10__int_2,dt_c5_10__int_2,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__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc1_numerals,e4_10__int_2,e6_10__int_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0]),
    [interesting(0.8),file(int_2,e7_10__int_2),[file(int_2,e7_10__int_2)]]).

fof(e8_10__int_2,plain,(
    r2_int_1(c1_10__int_2,c3_10__int_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__int_2,e1_10__int_2,dt_c2_10__int_2,dt_c3_10__int_2,e2_10__int_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_int_1,t2_subset,t3_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,fc5_int_1,fc7_int_1,rc1_int_1,spc2_arithm,spc7_arithm,t3_arithm,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r2_int_1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_c1_10__int_2,dt_c3_10__int_2,dt_c4_10__int_2,dt_c5_10__int_2,cc4_int_1,fc2_int_1,fc3_int_1,rc2_int_1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,e7_10__int_2,d9_int_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.8),file(int_2,e8_10__int_2),[file(int_2,e8_10__int_2)]]).

fof(i5_10__int_2,theorem,(
    $true ),
    introduced(tautology,[file(int_2,i5_10__int_2)]),
    [interesting(0.8),trivial,file(int_2,i5_10__int_2)]).

fof(i4_10__int_2,plain,(
    r2_int_1(c1_10__int_2,c3_10__int_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_10__int_2,e1_10__int_2,dt_c2_10__int_2,dt_c3_10__int_2,e2_10__int_2])],[e8_10__int_2,i5_10__int_2]),
    [interesting(0.8),file(int_2,i4_10__int_2),[file(int_2,i4_10__int_2)]]).

fof(i3_10__int_2,plain,
    ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
      & r2_int_1(c2_10__int_2,c3_10__int_2) )
   => r2_int_1(c1_10__int_2,c3_10__int_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__int_2,dt_c2_10__int_2,dt_c3_10__int_2]),discharge_asm(discharge,[e1_10__int_2,e2_10__int_2])],[e1_10__int_2,e2_10__int_2,i4_10__int_2]),
    [interesting(0.8),file(int_2,i3_10__int_2),[file(int_2,i3_10__int_2)]]).

fof(i3_10_tmp__int_2,plain,
    ( v1_int_1(c3_10__int_2)
   => ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
        & r2_int_1(c2_10__int_2,c3_10__int_2) )
     => r2_int_1(c1_10__int_2,c3_10__int_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__int_2,dt_c2_10__int_2]),discharge_asm(discharge,[dt_c3_10__int_2])],[dt_c3_10__int_2,i3_10__int_2]),
    [interesting(0.8),i2_10__int_2]).

fof(i2_10__int_2,plain,(
    ! [A] : 
      ( v1_int_1(A)
     => ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
          & r2_int_1(c2_10__int_2,A) )
       => r2_int_1(c1_10__int_2,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_10__int_2,dt_c2_10__int_2])],[i3_10_tmp__int_2,dh_c3_10__int_2]),
    [interesting(0.8),file(int_2,i2_10__int_2),[file(int_2,i2_10__int_2)]]).

fof(i2_10_tmp__int_2,plain,
    ( v1_int_1(c2_10__int_2)
   => ! [A] : 
        ( v1_int_1(A)
       => ( ( r2_int_1(c1_10__int_2,c2_10__int_2)
            & r2_int_1(c2_10__int_2,A) )
         => r2_int_1(c1_10__int_2,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__int_2]),discharge_asm(discharge,[dt_c2_10__int_2])],[dt_c2_10__int_2,i2_10__int_2]),
    [interesting(0.8),i1_10__int_2]).

fof(i1_10__int_2,plain,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ( r2_int_1(c1_10__int_2,A)
              & r2_int_1(A,B) )
           => r2_int_1(c1_10__int_2,B) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_10__int_2])],[i2_10_tmp__int_2,dh_c2_10__int_2]),
    [interesting(0.8),file(int_2,i1_10__int_2),[file(int_2,i1_10__int_2)]]).

fof(i1_10_tmp__int_2,plain,
    ( v1_int_1(c1_10__int_2)
   => ! [A] : 
        ( v1_int_1(A)
       => ! [B] : 
            ( v1_int_1(B)
           => ( ( r2_int_1(c1_10__int_2,A)
                & r2_int_1(A,B) )
             => r2_int_1(c1_10__int_2,B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_10__int_2])],[dt_c1_10__int_2,i1_10__int_2]),
    [interesting(1),t13_int_2]).

fof(t13_int_2,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( v1_int_1(C)
             => ( ( r2_int_1(A,B)
                  & r2_int_1(B,C) )
               => r2_int_1(A,C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_10_tmp__int_2,dh_c1_10__int_2]),
    [interesting(1),file(int_2,t13_int_2),[file(int_2,t13_int_2)]]).