% Mizar ND problem: t2_ami_4,ami_4,44,33 
fof(dh_c1_2__ami_4,definition,
    ( ( v1_int_1(c1_2__ami_4)
     => ! [A] : 
          ( v1_int_1(A)
         => ( ( r1_xreal_0(0,c1_2__ami_4)
              & r1_xreal_0(0,A) )
           => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(A)) = k6_int_1(c1_2__ami_4,A)
              & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(A)) = k5_int_1(c1_2__ami_4,A) ) ) ) )
   => ! [B] : 
        ( v1_int_1(B)
       => ! [C] : 
            ( v1_int_1(C)
           => ( ( r1_xreal_0(0,B)
                & r1_xreal_0(0,C) )
             => ( k4_nat_1(k1_int_2(B),k1_int_2(C)) = k6_int_1(B,C)
                & k3_nat_1(k1_int_2(B),k1_int_2(C)) = k5_int_1(B,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__ami_4),file(ami_4,c1_2__ami_4)]),
    [interesting(0.8),axiom,file(ami_4,c1_2__ami_4)]).

fof(dh_c2_2__ami_4,definition,
    ( ( v1_int_1(c2_2__ami_4)
     => ( ( r1_xreal_0(0,c1_2__ami_4)
          & r1_xreal_0(0,c2_2__ami_4) )
       => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
          & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ) ) )
   => ! [A] : 
        ( v1_int_1(A)
       => ( ( r1_xreal_0(0,c1_2__ami_4)
            & r1_xreal_0(0,A) )
         => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(A)) = k6_int_1(c1_2__ami_4,A)
            & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(A)) = k5_int_1(c1_2__ami_4,A) ) ) ) ),
    introduced(definition,[new_symbol(c2_2__ami_4),file(ami_4,c2_2__ami_4)]),
    [interesting(0.8),axiom,file(ami_4,c2_2__ami_4)]).

fof(e1_2__ami_4,assumption,(
    r1_xreal_0(0,c1_2__ami_4) ),
    introduced(assumption,[file(ami_4,e1_2__ami_4)]),
    [interesting(0.8),axiom,file(ami_4,e1_2__ami_4)]).

fof(e2_2__ami_4,assumption,(
    r1_xreal_0(0,c2_2__ami_4) ),
    introduced(assumption,[file(ami_4,e2_2__ami_4)]),
    [interesting(0.8),axiom,file(ami_4,e2_2__ami_4)]).

fof(e1_2_1_1__ami_4,assumption,(
    ~ r1_xreal_0(c2_2__ami_4,0) ),
    introduced(assumption,[file(ami_4,e1_2_1_1__ami_4)]),
    [interesting(0.5),axiom,file(ami_4,e1_2_1_1__ami_4)]).

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(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(fc10_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]).

fof(fc11_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]).

fof(fc12_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc12_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(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(fc7_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]).

fof(fc9_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]).

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_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(projectivity_k16_complex1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ),
    file(complex1,k16_complex1),
    [interesting(0.9),axiom,file(complex1,k16_complex1)]).

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_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k16_complex1(A)) ) ),
    file(complex1,k16_complex1),
    [interesting(0.9),axiom,file(complex1,k16_complex1)]).

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

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(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_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(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(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(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_int_1,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v1_int_1(k2_xcmplx_0(A,B)) ) ) ),
    file(int_1,fc1_int_1),
    [interesting(0.9),axiom,file(int_1,fc1_int_1)]).

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(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(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_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(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(fc3_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]).

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(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_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_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(fc6_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    [interesting(0.9),axiom,file(int_1,fc6_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(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(fc8_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]).

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_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_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

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

fof(spc1_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ),
    file(arithm,spc1_arithm),
    [interesting(0.9),axiom,file(arithm,spc1_arithm)]).

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(spc5_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ),
    file(arithm,spc5_arithm),
    [interesting(0.9),axiom,file(arithm,spc5_arithm)]).

fof(spc6_arithm,theorem,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ),
    file(arithm,spc6_arithm),
    [interesting(0.9),axiom,file(arithm,spc6_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(spc8_arithm,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ),
    file(arithm,spc8_arithm),
    [interesting(0.9),axiom,file(arithm,spc8_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_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    [interesting(0.9),axiom,file(arithm,t1_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(projectivity_k1_int_2,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => k1_int_2(k1_int_2(A)) = k1_int_2(A) ) ),
    file(int_2,k1_int_2),
    [interesting(0.9),axiom,file(int_2,k1_int_2)]).

fof(commutativity_k2_xcmplx_0,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

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_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_k1_int_2,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => k1_int_2(A) = k16_complex1(A) ) ),
    file(int_2,k1_int_2),
    [interesting(0.9),axiom,file(int_2,k1_int_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_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_int_2,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => m2_subset_1(k1_int_2(A),k1_numbers,k5_numbers) ) ),
    file(int_2,k1_int_2),
    [interesting(0.9),axiom,file(int_2,k1_int_2)]).

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

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]).

fof(dt_k3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => m2_subset_1(k3_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k3_nat_1),
    [interesting(0.9),axiom,file(nat_1,k3_nat_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_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => m2_subset_1(k4_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k4_nat_1),
    [interesting(0.9),axiom,file(nat_1,k4_nat_1)]).

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_int_1,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => v1_int_1(k5_int_1(A,B)) ) ),
    file(int_1,k5_int_1),
    [interesting(0.9),axiom,file(int_1,k5_int_1)]).

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_int_1,axiom,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => v1_int_1(k6_int_1(A,B)) ) ),
    file(int_1,k6_int_1),
    [interesting(0.9),axiom,file(int_1,k6_int_1)]).

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_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_2__ami_4,assumption,(
    v1_int_1(c1_2__ami_4) ),
    introduced(assumption,[file(ami_4,c1_2__ami_4)]),
    [interesting(0.8),axiom,file(ami_4,c1_2__ami_4)]).

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(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(dt_c2_2__ami_4,assumption,(
    v1_int_1(c2_2__ami_4) ),
    introduced(assumption,[file(ami_4,c2_2__ami_4)]),
    [interesting(0.8),axiom,file(ami_4,c2_2__ami_4)]).

fof(fc1_numbers,theorem,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    [interesting(0.9),axiom,file(numbers,fc1_numbers)]).

fof(de_c1_2_1_1__ami_4,definition,(
    c1_2_1_1__ami_4 = k6_int_1(c1_2__ami_4,c2_2__ami_4) ),
    introduced(definition,[new_symbol(c1_2_1_1__ami_4),file(ami_4,c1_2_1_1__ami_4)]),
    [interesting(0.5),axiom,file(ami_4,c1_2_1_1__ami_4)]).

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(t1_ami_4,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => r1_xreal_0(0,k5_int_1(A,B)) ) ) ) ),
    file(ami_4,t1_ami_4),
    [interesting(0.9),axiom,file(ami_4,t1_ami_4)]).

fof(t78_newton,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r1_xreal_0(0,A)
           => r1_xreal_0(0,k6_int_1(B,A)) ) ) ) ),
    file(newton,t78_newton),
    [interesting(0.9),axiom,file(newton,t78_newton)]).

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(e3_2_1_1__ami_4,plain,
    ( r1_xreal_0(0,k6_int_1(c1_2__ami_4,c2_2__ami_4))
    & r1_xreal_0(0,k5_int_1(c1_2__ami_4,c2_2__ami_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2__ami_4,e1_2_1_1__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc2_xreal_0,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,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_int_1,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k5_int_1,dt_k6_int_1,dt_c1_2__ami_4,dt_c2_2__ami_4,cc4_int_1,rc2_int_1,spc0_numerals,spc0_boole,e1_2__ami_4,e1_2_1_1__ami_4,t1_ami_4,t78_newton,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(ami_4,e3_2_1_1__ami_4),[file(ami_4,e3_2_1_1__ami_4)]]).

fof(t16_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( r1_xreal_0(0,A)
       => r2_hidden(A,k5_numbers) ) ) ),
    file(int_1,t16_int_1),
    [interesting(0.9),axiom,file(int_1,t16_int_1)]).

fof(e4_2_1_1__ami_4,plain,
    ( m2_subset_1(k6_int_1(c1_2__ami_4,c2_2__ami_4),k1_numbers,k5_numbers)
    & m2_subset_1(k5_int_1(c1_2__ami_4,c2_2__ami_4),k1_numbers,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2__ami_4,e1_2_1_1__ami_4])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_ordinal2,rc1_int_1,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_int_1,dt_k5_numbers,dt_k6_int_1,dt_m2_subset_1,dt_c1_2__ami_4,dt_c2_2__ami_4,cc4_int_1,fc1_numbers,rc2_int_1,t1_subset,t7_boole,spc0_numerals,spc0_boole,e3_2_1_1__ami_4,t16_int_1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(ami_4,e4_2_1_1__ami_4),[file(ami_4,e4_2_1_1__ami_4)]]).

fof(dt_c1_2_1_1__ami_4,plain,(
    m2_subset_1(c1_2_1_1__ami_4,k1_numbers,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2__ami_4,e1_2_1_1__ami_4])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_int_1,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_int_1,cc4_int_1,fc1_ordinal2,rc2_int_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_int_1,dt_k5_numbers,dt_k6_int_1,dt_m2_subset_1,dt_c1_2__ami_4,dt_c2_2__ami_4,fc1_numbers,de_c1_2_1_1__ami_4,e4_2_1_1__ami_4]),
    [interesting(0.5),file(ami_4,c1_2_1_1__ami_4),[file(ami_4,c1_2_1_1__ami_4)]]).

fof(de_c2_2_1_1__ami_4,definition,(
    c2_2_1_1__ami_4 = k5_int_1(c1_2__ami_4,c2_2__ami_4) ),
    introduced(definition,[new_symbol(c2_2_1_1__ami_4),file(ami_4,c2_2_1_1__ami_4)]),
    [interesting(0.5),axiom,file(ami_4,c2_2_1_1__ami_4)]).

fof(dt_c2_2_1_1__ami_4,plain,(
    m2_subset_1(c2_2_1_1__ami_4,k1_numbers,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2__ami_4,e1_2_1_1__ami_4])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_int_1,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_int_1,cc4_int_1,fc1_ordinal2,rc2_int_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_int_1,dt_k5_numbers,dt_k6_int_1,dt_m2_subset_1,dt_c1_2__ami_4,dt_c2_2__ami_4,fc1_numbers,de_c2_2_1_1__ami_4,e4_2_1_1__ami_4]),
    [interesting(0.5),file(ami_4,c2_2_1_1__ami_4),[file(ami_4,c2_2_1_1__ami_4)]]).

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(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,(
    k2_xcmplx_0(0,0) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,(
    k2_xcmplx_0(0,1) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,theorem,(
    k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,(
    k2_xcmplx_0(1,0) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]).

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(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(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(rqRealAdd__k2_xcmplx_0__r0_r2_r2,theorem,(
    k2_xcmplx_0(0,2) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,theorem,(
    k2_xcmplx_0(0,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,(
    k2_xcmplx_0(1,1) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2,theorem,(
    k2_xcmplx_0(2,0) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1,theorem,(
    k2_xcmplx_0(2,k4_xcmplx_0(1)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0,theorem,(
    k2_xcmplx_0(2,k4_xcmplx_0(2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),2) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),2) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,(
    k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,(
    k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,(
    k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,(
    k6_xcmplx_0(2,0) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,(
    k6_xcmplx_0(2,1) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,(
    k6_xcmplx_0(2,2) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_r2_r0,theorem,(
    k3_xcmplx_0(0,2) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0,theorem,(
    k3_xcmplx_0(0,k4_xcmplx_0(2)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0)]).

fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,(
    k3_xcmplx_0(1,2) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]).

fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2,theorem,(
    k3_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]).

fof(rqRealMult__k3_xcmplx_0__r2_r0_r0,theorem,(
    k3_xcmplx_0(2,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,(
    k3_xcmplx_0(2,1) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]).

fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]).

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(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,(
    k4_xcmplx_0(2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]).

fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]).

fof(spc2_numerals,theorem,
    ( v2_xreal_0(2)
    & m2_subset_1(2,k1_numbers,k5_numbers)
    & m1_subset_1(2,k5_numbers)
    & m1_subset_1(2,k1_numbers) ),
    file(numerals,spc2_numerals),
    [interesting(0.9),axiom,file(numerals,spc2_numerals)]).

fof(spc2_boole,theorem,(
    ~ v1_xboole_0(2) ),
    file(boole,spc2_boole),
    [interesting(0.9),axiom,file(boole,spc2_boole)]).

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_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(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(d8_int_1,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ( B != 0
             => k6_int_1(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) )
            & ( B = 0
             => k6_int_1(A,B) = 0 ) ) ) ) ),
    file(int_1,d8_int_1),
    [interesting(0.9),axiom,file(int_1,d8_int_1)]).

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(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(e6_2_1_1__ami_4,plain,(
    c1_2_1_1__ami_4 = k6_xcmplx_0(c1_2__ami_4,k3_xcmplx_0(c2_2_1_1__ami_4,c2_2__ami_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2__ami_4,e1_2_1_1__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_ordinal2,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_numbers,fc1_xreal_0,fc23_xreal_0,fc4_xreal_0,fc5_int_1,fc5_xreal_0,fc7_int_1,fc8_int_1,fc9_int_1,rc1_int_1,rc1_xreal_0,spc2_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,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,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k5_int_1,dt_k6_int_1,dt_k6_xcmplx_0,dt_c1_2__ami_4,dt_c1_2_1_1__ami_4,dt_c2_2__ami_4,dt_c2_2_1_1__ami_4,de_c1_2_1_1__ami_4,de_c2_2_1_1__ami_4,cc4_int_1,fc2_int_1,fc3_int_1,fc4_int_1,rc2_int_1,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__r1_r1_r0,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,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_2_1_1__ami_4,d8_int_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ami_4,e6_2_1_1__ami_4),[file(ami_4,e6_2_1_1__ami_4)]]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]).

fof(e7_2_1_1__ami_4,plain,(
    c1_2__ami_4 = k2_xcmplx_0(k3_xcmplx_0(c2_2__ami_4,c2_2_1_1__ami_4),c1_2_1_1__ami_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2__ami_4,e1_2_1_1__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_ordinal2,fc1_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_xreal_0,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_xreal_0,rc2_xreal_0,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_k5_int_1,dt_k5_numbers,dt_k6_int_1,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,cc4_int_1,fc1_int_1,fc1_numbers,fc2_int_1,fc3_int_1,fc4_int_1,fc5_int_1,fc6_int_1,fc7_int_1,fc8_int_1,fc9_int_1,rc2_int_1,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_2__ami_4,dt_c1_2_1_1__ami_4,dt_c2_2__ami_4,dt_c2_2_1_1__ami_4,de_c1_2_1_1__ami_4,de_c2_2_1_1__ami_4,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__rm2_r2,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e6_2_1_1__ami_4,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0]),
    [interesting(0.5),file(ami_4,e7_2_1_1__ami_4),[file(ami_4,e7_2_1_1__ami_4)]]).

fof(d1_absvalue,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r1_xreal_0(0,A)
         => k16_complex1(A) = A )
        & ( ~ r1_xreal_0(0,A)
         => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ),
    file(absvalue,d1_absvalue),
    [interesting(0.9),axiom,file(absvalue,d1_absvalue)]).

fof(e2_2_1_1__ami_4,plain,
    ( c1_2__ami_4 = k1_int_2(c1_2__ami_4)
    & c2_2__ami_4 = k1_int_2(c2_2__ami_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4,e1_2_1_1__ami_4,e1_2__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_xreal_0,fc1_ordinal2,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,cc3_xreal_0,cc4_int_1,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc1_numbers,fc3_int_1,fc5_int_1,rc1_int_1,rc1_xreal_0,rc2_int_1,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,projectivity_k16_complex1,projectivity_k1_int_2,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_int_2,dt_k16_complex1,dt_k1_int_2,dt_k4_xcmplx_0,dt_c1_2__ami_4,dt_c2_2__ami_4,cc2_xreal_0,fc1_xreal_0,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc0_boole,e1_2_1_1__ami_4,e1_2__ami_4,d1_absvalue,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(ami_4,e2_2_1_1__ami_4),[file(ami_4,e2_2_1_1__ami_4)]]).

fof(t79_newton,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(A,k6_int_1(B,A)) ) ) ) ),
    file(newton,t79_newton),
    [interesting(0.9),axiom,file(newton,t79_newton)]).

fof(e5_2_1_1__ami_4,plain,(
    ~ r1_xreal_0(c2_2__ami_4,c1_2_1_1__ami_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,e1_2__ami_4,dt_c2_2__ami_4,e1_2_1_1__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_2__ami_4,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_int_1,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k6_int_1,dt_c1_2_1_1__ami_4,dt_c2_2__ami_4,de_c1_2_1_1__ami_4,cc4_int_1,rc2_int_1,spc0_numerals,spc0_boole,e1_2_1_1__ami_4,t79_newton,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(ami_4,e5_2_1_1__ami_4),[file(ami_4,e5_2_1_1__ami_4)]]).

fof(d1_nat_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k3_nat_1(A,B)
              <=> ~ ( ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),D)
                            & ~ r1_xreal_0(B,D) ) )
                    & ~ ( C = 0
                        & B = 0 ) ) ) ) ) ) ),
    file(nat_1,d1_nat_1),
    [interesting(0.9),axiom,file(nat_1,d1_nat_1)]).

fof(d2_nat_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k4_nat_1(A,B)
              <=> ~ ( ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,D),C)
                            & ~ r1_xreal_0(B,C) ) )
                    & ~ ( C = 0
                        & B = 0 ) ) ) ) ) ) ),
    file(nat_1,d2_nat_1),
    [interesting(0.9),axiom,file(nat_1,d2_nat_1)]).

fof(e8_2_1_1__ami_4,plain,
    ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
    & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4,e1_2__ami_4,dt_c2_2__ami_4,e1_2_1_1__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,projectivity_k16_complex1,existence_m1_subset_1,dt_k16_complex1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_int_1,fc1_ordinal2,fc1_xreal_0,fc23_xreal_0,fc2_int_1,fc3_int_1,fc3_xreal_0,fc4_int_1,fc4_xreal_0,fc5_int_1,fc5_xreal_0,fc6_int_1,fc7_int_1,fc8_int_1,fc8_xreal_0,fc9_int_1,rc1_int_1,rc1_xreal_0,rc2_int_1,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,projectivity_k1_int_2,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k1_int_2,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_int_2,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_nat_1,dt_k3_xcmplx_0,dt_k4_nat_1,dt_k4_xcmplx_0,dt_k5_int_1,dt_k5_numbers,dt_k6_int_1,dt_k6_xcmplx_0,dt_m2_subset_1,dt_c1_2__ami_4,dt_c1_2_1_1__ami_4,dt_c2_2__ami_4,dt_c2_2_1_1__ami_4,de_c1_2_1_1__ami_4,de_c2_2_1_1__ami_4,cc1_xreal_0,cc3_int_1,fc1_numbers,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,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,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,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,e7_2_1_1__ami_4,e2_2_1_1__ami_4,e5_2_1_1__ami_4,d1_nat_1,d2_nat_1,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,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0]),
    [interesting(0.5),file(ami_4,e8_2_1_1__ami_4),[file(ami_4,e8_2_1_1__ami_4)]]).

fof(i2_2_1_1__ami_4,theorem,(
    $true ),
    introduced(tautology,[file(ami_4,i2_2_1_1__ami_4)]),
    [interesting(0.5),trivial,file(ami_4,i2_2_1_1__ami_4)]).

fof(i1_2_1_1__ami_4,plain,
    ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
    & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2__ami_4,e1_2__ami_4,dt_c2_2__ami_4,e1_2_1_1__ami_4])],[e8_2_1_1__ami_4,i2_2_1_1__ami_4]),
    [interesting(0.5),file(ami_4,i1_2_1_1__ami_4),[file(ami_4,i1_2_1_1__ami_4)]]).

fof(i1_2_1__ami_4,plain,
    ( ~ r1_xreal_0(c2_2__ami_4,0)
   => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
      & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ami_4,e1_2__ami_4,dt_c2_2__ami_4]),discharge_asm(discharge,[e1_2_1_1__ami_4])],[e1_2_1_1__ami_4,i1_2_1_1__ami_4]),
    [interesting(0.65),file(ami_4,i1_2_1__ami_4),[file(ami_4,i1_2_1__ami_4)]]).

fof(e1_2_1_2__ami_4,assumption,(
    c2_2__ami_4 = 0 ),
    introduced(assumption,[file(ami_4,e1_2_1_2__ami_4)]),
    [interesting(0.5),axiom,file(ami_4,e1_2_1_2__ami_4)]).

fof(e2_2_1_2__ami_4,plain,(
    k1_int_2(0) = 0 ),
    inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_xreal_0,fc1_ordinal2,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,cc3_xreal_0,cc4_int_1,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc1_numbers,fc3_int_1,fc5_int_1,rc1_int_1,rc1_xreal_0,rc2_int_1,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,projectivity_k16_complex1,projectivity_k1_int_2,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_int_2,dt_k16_complex1,dt_k1_int_2,dt_k4_xcmplx_0,cc2_xreal_0,fc1_xreal_0,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc0_boole,d1_absvalue,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(ami_4,e2_2_1_2__ami_4),[file(ami_4,e2_2_1_2__ami_4)]]).

fof(e3_2_1_2__ami_4,plain,
    ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(0)) = 0
    & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(0)) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,projectivity_k16_complex1,existence_m1_subset_1,dt_k16_complex1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc6_xreal_0,cc7_xreal_0,fc1_int_1,fc1_ordinal2,fc23_xreal_0,fc2_int_1,fc3_xreal_0,fc4_xreal_0,fc6_int_1,fc7_int_1,fc8_xreal_0,rc1_int_1,rc1_xreal_0,rc2_int_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,projectivity_k1_int_2,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k1_int_2,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_int_2,dt_k1_numbers,dt_k2_xcmplx_0,dt_k3_nat_1,dt_k3_xcmplx_0,dt_k4_nat_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_2__ami_4,cc1_xreal_0,cc3_int_1,fc1_numbers,rqLessOrEqual__r1_xreal_0__r0_r0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc0_numerals,spc0_boole,e2_2_1_2__ami_4,d1_nat_1,d2_nat_1]),
    [interesting(0.5),file(ami_4,e3_2_1_2__ami_4),[file(ami_4,e3_2_1_2__ami_4)]]).

fof(t75_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => k5_int_1(A,0) = 0 ) ),
    file(int_1,t75_int_1),
    [interesting(0.9),axiom,file(int_1,t75_int_1)]).

fof(e4_2_1_2__ami_4,plain,
    ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
    & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ami_4,dt_c1_2__ami_4,e1_2_1_2__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_ordinal2,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,projectivity_k16_complex1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k16_complex1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xreal_0,cc2_int_1,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_numbers,fc23_xreal_0,fc4_xreal_0,fc5_xreal_0,fc7_int_1,fc8_int_1,fc9_int_1,rc1_int_1,rc1_xreal_0,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t4_arithm,t6_boole,t7_boole,t8_boole,projectivity_k1_int_2,commutativity_k3_xcmplx_0,redefinition_k1_int_2,dt_k1_int_2,dt_k3_nat_1,dt_k3_xcmplx_0,dt_k4_nat_1,dt_k5_int_1,dt_k6_int_1,dt_k6_xcmplx_0,dt_c1_2__ami_4,dt_c2_2__ami_4,cc4_int_1,fc2_int_1,fc4_int_1,rc2_int_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,spc0_numerals,spc0_boole,e3_2_1_2__ami_4,e1_2_1_2__ami_4,t75_int_1,d8_int_1]),
    [interesting(0.5),file(ami_4,e4_2_1_2__ami_4),[file(ami_4,e4_2_1_2__ami_4)]]).

fof(i2_2_1_2__ami_4,theorem,(
    $true ),
    introduced(tautology,[file(ami_4,i2_2_1_2__ami_4)]),
    [interesting(0.5),trivial,file(ami_4,i2_2_1_2__ami_4)]).

fof(i1_2_1_2__ami_4,plain,
    ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
    & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_2__ami_4,dt_c1_2__ami_4,e1_2_1_2__ami_4])],[e4_2_1_2__ami_4,i2_2_1_2__ami_4]),
    [interesting(0.5),file(ami_4,i1_2_1_2__ami_4),[file(ami_4,i1_2_1_2__ami_4)]]).

fof(i2_2_1__ami_4,plain,
    ( c2_2__ami_4 = 0
   => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
      & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ami_4,dt_c1_2__ami_4]),discharge_asm(discharge,[e1_2_1_2__ami_4])],[e1_2_1_2__ami_4,i1_2_1_2__ami_4]),
    [interesting(0.65),file(ami_4,i2_2_1__ami_4),[file(ami_4,i2_2_1__ami_4)]]).

fof(e1_2_1__ami_4,plain,(
    ~ ( r1_xreal_0(c2_2__ami_4,0)
      & c2_2__ami_4 != 0 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ami_4,e2_2__ami_4])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc1_xreal_0,cc3_int_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_int_1,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_int_1,cc2_xreal_0,cc3_xreal_0,cc4_int_1,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc2_int_1,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c2_2__ami_4,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e2_2__ami_4]),
    [interesting(0.65),file(ami_4,e1_2_1__ami_4),[file(ami_4,e1_2_1__ami_4)]]).

fof(i2_2__ami_4,plain,
    ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
    & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ),
    inference(percases,[status(thm),assumptions([e1_2__ami_4,dt_c1_2__ami_4,dt_c2_2__ami_4,e2_2__ami_4])],[i1_2_1__ami_4,i2_2_1__ami_4,e1_2_1__ami_4]),
    [interesting(0.8),file(ami_4,i2_2__ami_4),[file(ami_4,i2_2__ami_4)]]).

fof(i1_2__ami_4,plain,
    ( ( r1_xreal_0(0,c1_2__ami_4)
      & r1_xreal_0(0,c2_2__ami_4) )
   => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
      & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ami_4,dt_c2_2__ami_4]),discharge_asm(discharge,[e1_2__ami_4,e2_2__ami_4])],[e1_2__ami_4,e2_2__ami_4,i2_2__ami_4]),
    [interesting(0.8),file(ami_4,i1_2__ami_4),[file(ami_4,i1_2__ami_4)]]).

fof(i1_2_tmp__ami_4,plain,
    ( ( v1_int_1(c1_2__ami_4)
      & v1_int_1(c2_2__ami_4) )
   => ( ( r1_xreal_0(0,c1_2__ami_4)
        & r1_xreal_0(0,c2_2__ami_4) )
     => ( k4_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k6_int_1(c1_2__ami_4,c2_2__ami_4)
        & k3_nat_1(k1_int_2(c1_2__ami_4),k1_int_2(c2_2__ami_4)) = k5_int_1(c1_2__ami_4,c2_2__ami_4) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__ami_4,dt_c2_2__ami_4])],[dt_c1_2__ami_4,dt_c2_2__ami_4,i1_2__ami_4]),
    [interesting(1),t2_ami_4]).

fof(t2_ami_4,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( ( r1_xreal_0(0,A)
              & r1_xreal_0(0,B) )
           => ( k4_nat_1(k1_int_2(A),k1_int_2(B)) = k6_int_1(A,B)
              & k3_nat_1(k1_int_2(A),k1_int_2(B)) = k5_int_1(A,B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__ami_4,dh_c1_2__ami_4,dh_c2_2__ami_4]),
    [interesting(1),file(ami_4,t2_ami_4),[file(ami_4,t2_ami_4)]]).