% Mizar ND problem: t8_rcomp_1,rcomp_1,131,27 
fof(dh_c1_8__rcomp_1,definition,
    ( ( v1_xreal_0(c1_8__rcomp_1)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ! [B] : 
              ( v1_xreal_0(B)
             => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)))
              <=> ~ r1_xreal_0(B,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,A))) ) ) ) )
   => ! [C] : 
        ( v1_xreal_0(C)
       => ! [D] : 
            ( v1_xreal_0(D)
           => ! [E] : 
                ( v1_xreal_0(E)
               => ( r2_hidden(C,k2_rcomp_1(k6_xcmplx_0(D,E),k2_xcmplx_0(D,E)))
                <=> ~ r1_xreal_0(E,k18_complex1(k6_xcmplx_0(C,D))) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_8__rcomp_1),file(rcomp_1,c1_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,c1_8__rcomp_1)]).

fof(dh_c2_8__rcomp_1,definition,
    ( ( v1_xreal_0(c2_8__rcomp_1)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,A),k2_xcmplx_0(c2_8__rcomp_1,A)))
          <=> ~ r1_xreal_0(A,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( v1_xreal_0(C)
           => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(B,C),k2_xcmplx_0(B,C)))
            <=> ~ r1_xreal_0(C,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,B))) ) ) ) ),
    introduced(definition,[new_symbol(c2_8__rcomp_1),file(rcomp_1,c2_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,c2_8__rcomp_1)]).

fof(dh_c3_8__rcomp_1,definition,
    ( ( v1_xreal_0(c3_8__rcomp_1)
     => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1)))
      <=> ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) )
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,A),k2_xcmplx_0(c2_8__rcomp_1,A)))
        <=> ~ r1_xreal_0(A,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) ) ),
    introduced(definition,[new_symbol(c3_8__rcomp_1),file(rcomp_1,c3_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,c3_8__rcomp_1)]).

fof(e1_8_1__rcomp_1,assumption,(
    r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1))) ),
    introduced(assumption,[file(rcomp_1,e1_8_1__rcomp_1)]),
    [interesting(0.65),axiom,file(rcomp_1,e1_8_1__rcomp_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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

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

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

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

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

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

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

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

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

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

fof(fc14_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A))
        & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc14_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc14_xreal_0)]).

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

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

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

fof(fc1_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(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(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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

fof(rc2_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

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

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

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

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

fof(t5_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(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_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_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(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

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

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(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(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(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(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_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

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

fof(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_k18_complex1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ),
    file(complex1,k18_complex1),
    [interesting(0.9),axiom,file(complex1,k18_complex1)]).

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(redefinition_k18_complex1,definition,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k18_complex1(A) = k16_complex1(A) ) ),
    file(complex1,k18_complex1),
    [interesting(0.9),axiom,file(complex1,k18_complex1)]).

fof(dt_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => m1_subset_1(k18_complex1(A),k1_numbers) ) ),
    file(complex1,k18_complex1),
    [interesting(0.9),axiom,file(complex1,k18_complex1)]).

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

fof(dt_c1_8__rcomp_1,assumption,(
    v1_xreal_0(c1_8__rcomp_1) ),
    introduced(assumption,[file(rcomp_1,c1_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,c1_8__rcomp_1)]).

fof(dt_c2_8__rcomp_1,assumption,(
    v1_xreal_0(c2_8__rcomp_1) ),
    introduced(assumption,[file(rcomp_1,c2_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,c2_8__rcomp_1)]).

fof(dt_c3_8__rcomp_1,assumption,(
    v1_xreal_0(c3_8__rcomp_1) ),
    introduced(assumption,[file(rcomp_1,c3_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,c3_8__rcomp_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(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(fc5_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc5_xreal_0)]).

fof(rqLessOrEqual__r1_xreal_0__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_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(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(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

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(fc1_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]).

fof(fc3_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]).

fof(fc4_nat_1,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]).

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

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(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_2_2_rcomp_1,definition,(
    ! [A,B,C] : 
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_2_rcomp_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_numbers)
            & A = D
            & ~ r1_xreal_0(D,k6_xcmplx_0(B,C))
            & ~ r1_xreal_0(k2_xcmplx_0(B,C),D) ) ) ) ),
    file(rcomp_1,a_2_2_rcomp_1),
    [interesting(0.9),axiom,file(rcomp_1,a_2_2_rcomp_1)]).

fof(fraenkel_a_2_1_rcomp_1,definition,(
    ! [A,B,C] : 
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_1_rcomp_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k1_numbers)
            & A = D
            & ~ r1_xreal_0(D,B)
            & ~ r1_xreal_0(C,D) ) ) ) ),
    file(rcomp_1,a_2_1_rcomp_1),
    [interesting(0.9),axiom,file(rcomp_1,a_2_1_rcomp_1)]).

fof(dt_k2_rcomp_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) ),
    file(rcomp_1,k2_rcomp_1),
    [interesting(0.9),axiom,file(rcomp_1,k2_rcomp_1)]).

fof(d2_rcomp_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k2_rcomp_1(A,B) = a_2_1_rcomp_1(A,B) ) ) ),
    file(rcomp_1,d2_rcomp_1),
    [interesting(0.9),axiom,file(rcomp_1,d2_rcomp_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(e2_8_1__rcomp_1,plain,(
    r2_hidden(c1_8__rcomp_1,a_2_2_rcomp_1(c2_8__rcomp_1,c3_8__rcomp_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,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,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_xreal_0,fc2_membered,fc3_xreal_0,fc5_xreal_0,fc8_xreal_0,rc1_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,fraenkel_a_2_1_rcomp_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,dt_k2_rcomp_1,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,rqRealNeg__k4_xcmplx_0__rm1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_2_rcomp_1,d2_rcomp_1,spc1_numerals,spc1_boole,e1_8_1__rcomp_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.65),file(rcomp_1,e2_8_1__rcomp_1),[file(rcomp_1,e2_8_1__rcomp_1)]]).

fof(e3_8_1__rcomp_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & c1_8__rcomp_1 = A
      & ~ r1_xreal_0(A,k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1))
      & ~ r1_xreal_0(k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_xreal_0,fc3_xreal_0,fc5_xreal_0,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_m1_subset_1,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_2_rcomp_1,spc1_numerals,spc1_boole,e2_8_1__rcomp_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.65),file(rcomp_1,e3_8_1__rcomp_1),[file(rcomp_1,e3_8_1__rcomp_1)]]).

fof(t21_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(k2_xcmplx_0(A,B),C)
              <=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ),
    file(xreal_1,t21_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t21_xreal_1)]).

fof(e6_8_1__rcomp_1,plain,(
    ~ r1_xreal_0(c3_8__rcomp_1,k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_nat_1,cc2_nat_1,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_m1_subset_1,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,cc2_xreal_0,fc1_xreal_0,fc2_membered,fc3_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e3_8_1__rcomp_1,t21_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.65),file(rcomp_1,e6_8_1__rcomp_1),[file(rcomp_1,e6_8_1__rcomp_1)]]).

fof(e4_8_1__rcomp_1,plain,(
    ~ r1_xreal_0(c1_8__rcomp_1,k2_xcmplx_0(c2_8__rcomp_1,k4_xcmplx_0(c3_8__rcomp_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_xreal_0,fc3_xreal_0,fc5_xreal_0,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_m1_subset_1,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e3_8_1__rcomp_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.65),file(rcomp_1,e4_8_1__rcomp_1),[file(rcomp_1,e4_8_1__rcomp_1)]]).

fof(t22_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,k2_xcmplx_0(B,C))
              <=> r1_xreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) ),
    file(xreal_1,t22_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t22_xreal_1)]).

fof(e5_8_1__rcomp_1,plain,(
    ~ r1_xreal_0(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1),k4_xcmplx_0(c3_8__rcomp_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,cc2_xreal_0,fc1_xreal_0,fc3_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e4_8_1__rcomp_1,t22_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.65),file(rcomp_1,e5_8_1__rcomp_1),[file(rcomp_1,e5_8_1__rcomp_1)]]).

fof(t9_seq_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
              & ~ r1_xreal_0(A,B) )
          <=> ~ r1_xreal_0(A,k18_complex1(B)) ) ) ) ),
    file(seq_2,t9_seq_2),
    [interesting(0.9),axiom,file(seq_2,t9_seq_2)]).

fof(e7_8_1__rcomp_1,plain,(
    ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_ordinal2,fc20_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,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,cc15_membered,cc1_nat_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,rc1_xreal_0,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,projectivity_k18_complex1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k18_complex1,dt_k18_complex1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,cc2_xreal_0,fc1_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e6_8_1__rcomp_1,e5_8_1__rcomp_1,t9_seq_2,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.65),file(rcomp_1,e7_8_1__rcomp_1),[file(rcomp_1,e7_8_1__rcomp_1)]]).

fof(i2_8_1__rcomp_1,theorem,(
    $true ),
    introduced(tautology,[file(rcomp_1,i2_8_1__rcomp_1)]),
    [interesting(0.65),trivial,file(rcomp_1,i2_8_1__rcomp_1)]).

fof(i1_8_1__rcomp_1,plain,(
    ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e1_8_1__rcomp_1])],[e7_8_1__rcomp_1,i2_8_1__rcomp_1]),
    [interesting(0.65),file(rcomp_1,i1_8_1__rcomp_1),[file(rcomp_1,i1_8_1__rcomp_1)]]).

fof(e1_8__rcomp_1,plain,(
    ~ ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1)))
      & r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1]),discharge_asm(discharge,[e1_8_1__rcomp_1])],[e1_8_1__rcomp_1,i1_8_1__rcomp_1]),
    [interesting(0.8),file(rcomp_1,e1_8__rcomp_1),[file(rcomp_1,e1_8__rcomp_1)]]).

fof(e3_8__rcomp_1,assumption,(
    ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ),
    introduced(assumption,[file(rcomp_1,e3_8__rcomp_1)]),
    [interesting(0.8),axiom,file(rcomp_1,e3_8__rcomp_1)]).

fof(e4_8__rcomp_1,plain,
    ( ~ r1_xreal_0(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1),k4_xcmplx_0(c3_8__rcomp_1))
    & ~ r1_xreal_0(c3_8__rcomp_1,k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e3_8__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_ordinal2,fc20_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,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,cc15_membered,cc1_nat_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,rc1_xreal_0,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,projectivity_k18_complex1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k18_complex1,dt_k18_complex1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,cc2_xreal_0,fc1_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e3_8__rcomp_1,t9_seq_2,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.8),file(rcomp_1,e4_8__rcomp_1),[file(rcomp_1,e4_8__rcomp_1)]]).

fof(e6_8__rcomp_1,plain,(
    ~ r1_xreal_0(k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),c1_8__rcomp_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e3_8__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,cc2_xreal_0,fc1_xreal_0,fc3_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e4_8__rcomp_1,t21_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.8),file(rcomp_1,e6_8__rcomp_1),[file(rcomp_1,e6_8__rcomp_1)]]).

fof(d1_xreal_0,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
    <=> r2_hidden(A,k1_numbers) ) ),
    file(xreal_0,d1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,d1_xreal_0)]).

fof(e2_8__rcomp_1,plain,(
    m1_subset_1(c1_8__rcomp_1,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1])],[cc1_xreal_0,cc3_nat_1,rc1_nat_1,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,cc10_membered,cc11_membered,cc15_membered,cc4_membered,cc7_xreal_0,rc1_xreal_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_numbers,dt_m1_subset_1,dt_c1_8__rcomp_1,cc2_xreal_0,fc2_membered,t1_subset,t7_boole,d1_xreal_0]),
    [interesting(0.8),file(rcomp_1,e2_8__rcomp_1),[file(rcomp_1,e2_8__rcomp_1)]]).

fof(e5_8__rcomp_1,plain,(
    ~ r1_xreal_0(c1_8__rcomp_1,k2_xcmplx_0(c2_8__rcomp_1,k4_xcmplx_0(c3_8__rcomp_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e3_8__rcomp_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_nat_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,cc2_xreal_0,fc1_xreal_0,fc3_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,spc1_numerals,spc1_boole,e4_8__rcomp_1,t22_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.8),file(rcomp_1,e5_8__rcomp_1),[file(rcomp_1,e5_8__rcomp_1)]]).

fof(e7_8__rcomp_1,plain,(
    r2_hidden(c1_8__rcomp_1,a_2_2_rcomp_1(c2_8__rcomp_1,c3_8__rcomp_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e3_8__rcomp_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_k6_xcmplx_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_xreal_0,fc3_xreal_0,fc5_xreal_0,fc8_xreal_0,rc1_xreal_0,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t4_real,t6_boole,t8_boole,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_m1_subset_1,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_2_rcomp_1,spc1_numerals,spc1_boole,e6_8__rcomp_1,e2_8__rcomp_1,e5_8__rcomp_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.8),file(rcomp_1,e7_8__rcomp_1),[file(rcomp_1,e7_8__rcomp_1)]]).

fof(e8_8__rcomp_1,plain,(
    r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e3_8__rcomp_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,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,fc1_nat_1,fc1_ordinal2,fc20_xreal_0,fc3_nat_1,fc4_nat_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_nat_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_nat_1,cc2_nat_1,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_xreal_0,fc2_membered,fc3_xreal_0,fc5_xreal_0,fc8_xreal_0,rc1_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,fraenkel_a_2_1_rcomp_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,dt_k2_rcomp_1,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,rqRealNeg__k4_xcmplx_0__rm1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_2_rcomp_1,d2_rcomp_1,spc1_numerals,spc1_boole,e7_8__rcomp_1,rqRealNeg__k4_xcmplx_0__r1_rm1]),
    [interesting(0.8),file(rcomp_1,e8_8__rcomp_1),[file(rcomp_1,e8_8__rcomp_1)]]).

fof(i6_8__rcomp_1,theorem,(
    $true ),
    introduced(tautology,[file(rcomp_1,i6_8__rcomp_1)]),
    [interesting(0.8),trivial,file(rcomp_1,i6_8__rcomp_1)]).

fof(i5_8__rcomp_1,plain,(
    r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1,e3_8__rcomp_1])],[e8_8__rcomp_1,i6_8__rcomp_1]),
    [interesting(0.8),file(rcomp_1,i5_8__rcomp_1),[file(rcomp_1,i5_8__rcomp_1)]]).

fof(i4_8__rcomp_1,plain,
    ( ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1)))
   => r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1]),discharge_asm(discharge,[e3_8__rcomp_1])],[e3_8__rcomp_1,i5_8__rcomp_1]),
    [interesting(0.8),file(rcomp_1,i4_8__rcomp_1),[file(rcomp_1,i4_8__rcomp_1)]]).

fof(i3_8__rcomp_1,plain,
    ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1)))
  <=> ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1,dt_c3_8__rcomp_1])],[e1_8__rcomp_1,i4_8__rcomp_1]),
    [interesting(0.8),file(rcomp_1,i3_8__rcomp_1),[file(rcomp_1,i3_8__rcomp_1)]]).

fof(i3_8_tmp__rcomp_1,plain,
    ( v1_xreal_0(c3_8__rcomp_1)
   => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1),k2_xcmplx_0(c2_8__rcomp_1,c3_8__rcomp_1)))
    <=> ~ r1_xreal_0(c3_8__rcomp_1,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1]),discharge_asm(discharge,[dt_c3_8__rcomp_1])],[dt_c3_8__rcomp_1,i3_8__rcomp_1]),
    [interesting(0.8),i2_8__rcomp_1]).

fof(i2_8__rcomp_1,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,A),k2_xcmplx_0(c2_8__rcomp_1,A)))
      <=> ~ r1_xreal_0(A,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__rcomp_1,dt_c2_8__rcomp_1])],[i3_8_tmp__rcomp_1,dh_c3_8__rcomp_1]),
    [interesting(0.8),file(rcomp_1,i2_8__rcomp_1),[file(rcomp_1,i2_8__rcomp_1)]]).

fof(i2_8_tmp__rcomp_1,plain,
    ( v1_xreal_0(c2_8__rcomp_1)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(c2_8__rcomp_1,A),k2_xcmplx_0(c2_8__rcomp_1,A)))
        <=> ~ r1_xreal_0(A,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,c2_8__rcomp_1))) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__rcomp_1]),discharge_asm(discharge,[dt_c2_8__rcomp_1])],[dt_c2_8__rcomp_1,i2_8__rcomp_1]),
    [interesting(0.8),i1_8__rcomp_1]).

fof(i1_8__rcomp_1,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)))
          <=> ~ r1_xreal_0(B,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,A))) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__rcomp_1])],[i2_8_tmp__rcomp_1,dh_c2_8__rcomp_1]),
    [interesting(0.8),file(rcomp_1,i1_8__rcomp_1),[file(rcomp_1,i1_8__rcomp_1)]]).

fof(i1_8_tmp__rcomp_1,plain,
    ( v1_xreal_0(c1_8__rcomp_1)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ! [B] : 
            ( v1_xreal_0(B)
           => ( r2_hidden(c1_8__rcomp_1,k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)))
            <=> ~ r1_xreal_0(B,k18_complex1(k6_xcmplx_0(c1_8__rcomp_1,A))) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__rcomp_1])],[dt_c1_8__rcomp_1,i1_8__rcomp_1]),
    [interesting(1),t8_rcomp_1]).

fof(t8_rcomp_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r2_hidden(A,k2_rcomp_1(k6_xcmplx_0(B,C),k2_xcmplx_0(B,C)))
              <=> ~ r1_xreal_0(C,k18_complex1(k6_xcmplx_0(A,B))) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__rcomp_1,dh_c1_8__rcomp_1]),
    [interesting(1),file(rcomp_1,t8_rcomp_1),[file(rcomp_1,t8_rcomp_1)]]).