% Mizar ND problem: t2_ali2,ali2,60,44 
fof(dh_c1_2__ali2,definition,
    ( ( ( ~ v3_struct_0(c1_2__ali2)
        & v6_metric_1(c1_2__ali2)
        & v7_metric_1(c1_2__ali2)
        & v8_metric_1(c1_2__ali2)
        & v9_metric_1(c1_2__ali2)
        & l1_metric_1(c1_2__ali2) )
     => ! [A] : 
          ( m1_ali2(A,c1_2__ali2)
         => ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
              & ! [B] : 
                  ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
                 => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),A,B) = B
                      & ! [C] : 
                          ( m1_subset_1(C,u1_struct_0(c1_2__ali2))
                         => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),A,C) = C
                           => C = B ) ) ) ) ) ) )
   => ! [D] : 
        ( ( ~ v3_struct_0(D)
          & v6_metric_1(D)
          & v7_metric_1(D)
          & v8_metric_1(D)
          & v9_metric_1(D)
          & l1_metric_1(D) )
       => ! [E] : 
            ( m1_ali2(E,D)
           => ~ ( v2_compts_1(k5_pcomps_1(D))
                & ! [F] : 
                    ( m1_subset_1(F,u1_struct_0(D))
                   => ~ ( k8_funct_2(u1_struct_0(D),u1_struct_0(D),E,F) = F
                        & ! [G] : 
                            ( m1_subset_1(G,u1_struct_0(D))
                           => ( k8_funct_2(u1_struct_0(D),u1_struct_0(D),E,G) = G
                             => G = F ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__ali2),file(ali2,c1_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c1_2__ali2)]).

fof(dh_c2_2__ali2,definition,
    ( ( m1_ali2(c2_2__ali2,c1_2__ali2)
     => ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
          & ! [A] : 
              ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
             => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
                  & ! [B] : 
                      ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
                     => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B) = B
                       => B = A ) ) ) ) ) )
   => ! [C] : 
        ( m1_ali2(C,c1_2__ali2)
       => ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
            & ! [D] : 
                ( m1_subset_1(D,u1_struct_0(c1_2__ali2))
               => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),C,D) = D
                    & ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(c1_2__ali2))
                       => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),C,E) = E
                         => E = D ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_2__ali2),file(ali2,c2_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c2_2__ali2)]).

fof(e4_2__ali2,assumption,(
    v2_compts_1(k5_pcomps_1(c1_2__ali2)) ),
    introduced(assumption,[file(ali2,e4_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,e4_2__ali2)]).

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

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(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_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_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(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(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_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_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(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(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_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(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_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(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_l1_metric_1,axiom,(
    ! [A] : 
      ( l1_metric_1(A)
     => l1_struct_0(A) ) ),
    file(metric_1,l1_metric_1),
    [interesting(0.9),axiom,file(metric_1,l1_metric_1)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_m1_ali2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] : 
          ( m1_ali2(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ) ),
    file(ali2,m1_ali2),
    [interesting(0.9),axiom,file(ali2,m1_ali2)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(redefinition_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

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_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_2__ali2,assumption,
    ( ~ v3_struct_0(c1_2__ali2)
    & v6_metric_1(c1_2__ali2)
    & v7_metric_1(c1_2__ali2)
    & v8_metric_1(c1_2__ali2)
    & v9_metric_1(c1_2__ali2)
    & l1_metric_1(c1_2__ali2) ),
    introduced(assumption,[file(ali2,c1_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c1_2__ali2)]).

fof(dt_c2_2__ali2,assumption,(
    m1_ali2(c2_2__ali2,c1_2__ali2) ),
    introduced(assumption,[file(ali2,c2_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c2_2__ali2)]).

fof(dh_c6_2__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
        & k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)) = 0 )
   => ( m1_subset_1(c6_2__ali2,u1_struct_0(c1_2__ali2))
      & k4_metric_1(c1_2__ali2,c6_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c6_2__ali2)) = 0 ) ),
    introduced(definition,[new_symbol(c6_2__ali2),file(ali2,c6_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c6_2__ali2)]).

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(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

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

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

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

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

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

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

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

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

fof(existence_l1_metric_1,axiom,(
    ? [A] : l1_metric_1(A) ),
    file(metric_1,l1_metric_1),
    [interesting(0.9),axiom,file(metric_1,l1_metric_1)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_m1_ali2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ? [B] : m1_ali2(B,A) ) ),
    file(ali2,m1_ali2),
    [interesting(0.9),axiom,file(ali2,m1_ali2)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

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

fof(dt_k2_metric_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_metric_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_metric_1(A,B,C),k1_numbers) ) ),
    file(metric_1,k2_metric_1),
    [interesting(0.9),axiom,file(metric_1,k2_metric_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_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(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(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

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

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

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

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

fof(commutativity_k4_metric_1,theorem,(
    ! [A,B,C] : 
      ( ( v8_metric_1(A)
        & l1_metric_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_metric_1(A,B,C) = k4_metric_1(A,C,B) ) ),
    file(metric_1,k4_metric_1),
    [interesting(0.9),axiom,file(metric_1,k4_metric_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(redefinition_k4_metric_1,definition,(
    ! [A,B,C] : 
      ( ( v8_metric_1(A)
        & l1_metric_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_metric_1(A,B,C) = k2_metric_1(A,B,C) ) ),
    file(metric_1,k4_metric_1),
    [interesting(0.9),axiom,file(metric_1,k4_metric_1)]).

fof(dt_k4_metric_1,axiom,(
    ! [A,B,C] : 
      ( ( v8_metric_1(A)
        & l1_metric_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_metric_1(A,B,C),k1_numbers) ) ),
    file(metric_1,k4_metric_1),
    [interesting(0.9),axiom,file(metric_1,k4_metric_1)]).

fof(dh_c4_2__ali2,definition,
    ( ? [A] : m1_subset_1(A,u1_struct_0(c1_2__ali2))
   => m1_subset_1(c4_2__ali2,u1_struct_0(c1_2__ali2)) ),
    introduced(definition,[new_symbol(c4_2__ali2),file(ali2,c4_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c4_2__ali2)]).

fof(e5_2__ali2,plain,(
    ? [A] : m1_subset_1(A,u1_struct_0(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t8_boole,cc15_membered,t2_subset,t6_boole,t7_boole,existence_l1_metric_1,existence_l1_struct_0,dt_l1_metric_1,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2]),
    [interesting(0.8),file(ali2,e5_2__ali2),[file(ali2,e5_2__ali2)]]).

fof(dt_c4_2__ali2,plain,(
    m1_subset_1(c4_2__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__ali2])],[dh_c4_2__ali2,e5_2__ali2]),
    [interesting(0.8),file(ali2,c4_2__ali2),[file(ali2,c4_2__ali2)]]).

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(e1_2_1__ali2,assumption,(
    k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)) != 0 ),
    introduced(assumption,[file(ali2,e1_2_1__ali2)]),
    [interesting(0.65),axiom,file(ali2,e1_2_1__ali2)]).

fof(free_g1_pre_topc,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,g1_pre_topc)]).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,g1_pre_topc)]).

fof(dt_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,u1_pre_topc)]).

fof(abstractness_v1_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,v1_pre_topc)]).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(dt_k5_pcomps_1,axiom,(
    ! [A] : 
      ( l1_metric_1(A)
     => l1_pre_topc(k5_pcomps_1(A)) ) ),
    file(pcomps_1,k5_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,k5_pcomps_1)]).

fof(fc3_pcomps_1,theorem,(
    ! [A] : 
      ( l1_metric_1(A)
     => ( v1_pre_topc(k5_pcomps_1(A))
        & v2_pre_topc(k5_pcomps_1(A)) ) ) ),
    file(pcomps_1,fc3_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,fc3_pcomps_1)]).

fof(fc4_pcomps_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_metric_1(A) )
     => ( ~ v3_struct_0(k5_pcomps_1(A))
        & v1_pre_topc(k5_pcomps_1(A))
        & v2_pre_topc(k5_pcomps_1(A)) ) ) ),
    file(pcomps_1,fc4_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,fc4_pcomps_1)]).

fof(dh_c2_2_1__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(k5_pcomps_1(c1_2__ali2)))
        & r2_hidden(A,k6_setfam_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1__ali2)) )
   => ( m1_subset_1(c2_2_1__ali2,u1_struct_0(k5_pcomps_1(c1_2__ali2)))
      & r2_hidden(c2_2_1__ali2,k6_setfam_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1__ali2)) ) ),
    introduced(definition,[new_symbol(c2_2_1__ali2),file(ali2,c2_2_1__ali2)]),
    [interesting(0.65),axiom,file(ali2,c2_2_1__ali2)]).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]).

fof(redefinition_k6_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

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

fof(dt_k3_power,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k3_power(A,B)) ) ),
    file(power,k3_power),
    [interesting(0.9),axiom,file(power,k3_power)]).

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

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

fof(commutativity_k4_real_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k4_real_1(B,A) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

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_k4_power,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_power(A,B) = k3_power(A,B) ) ),
    file(power,k4_power),
    [interesting(0.9),axiom,file(power,k4_power)]).

fof(redefinition_k4_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(dt_k4_power,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_power(A,B),k1_numbers) ) ),
    file(power,k4_power),
    [interesting(0.9),axiom,file(power,k4_power)]).

fof(dt_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ),
    file(real_1,k4_real_1),
    [interesting(0.9),axiom,file(real_1,k4_real_1)]).

fof(dh_c3_2__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & ~ r1_xreal_0(A,0)
        & ~ r1_xreal_0(1,A)
        & ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_2__ali2))
               => r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,C)),k4_real_1(A,k4_metric_1(c1_2__ali2,B,C))) ) ) )
   => ( m1_subset_1(c3_2__ali2,k1_numbers)
      & ~ r1_xreal_0(c3_2__ali2,0)
      & ~ r1_xreal_0(1,c3_2__ali2)
      & ! [D] : 
          ( m1_subset_1(D,u1_struct_0(c1_2__ali2))
         => ! [E] : 
              ( m1_subset_1(E,u1_struct_0(c1_2__ali2))
             => r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,D),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,E)),k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,D,E))) ) ) ) ),
    introduced(definition,[new_symbol(c3_2__ali2),file(ali2,c3_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c3_2__ali2)]).

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

fof(t5_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

fof(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

fof(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(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(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(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(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(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(d1_ali2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( m1_ali2(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,k1_numbers)
                & ~ r1_xreal_0(C,0)
                & ~ r1_xreal_0(1,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r1_xreal_0(k4_metric_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)),k4_real_1(C,k4_metric_1(A,D,E))) ) ) ) ) ) ) ),
    file(ali2,d1_ali2),
    [interesting(0.9),axiom,file(ali2,d1_ali2)]).

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(e1_2__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ~ r1_xreal_0(A,0)
      & ~ r1_xreal_0(1,A)
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_2__ali2))
             => r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,C)),k4_real_1(A,k4_metric_1(c1_2__ali2,B,C))) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,spc7_arithm,t1_subset,t2_arithm,t2_real,t3_arithm,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,existence_l1_struct_0,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k3_xcmplx_0,dt_k5_numbers,dt_l1_struct_0,dt_m1_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_subset_1,fc4_xreal_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r1_r1,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_ali2,existence_m1_subset_1,existence_m2_relset_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d1_ali2,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.8),file(ali2,e1_2__ali2),[file(ali2,e1_2__ali2)]]).

fof(dt_c3_2__ali2,plain,(
    m1_subset_1(c3_2__ali2,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[dh_c3_2__ali2,e1_2__ali2]),
    [interesting(0.8),file(ali2,c3_2__ali2),[file(ali2,c3_2__ali2)]]).

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_5_0_ali2,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(B)
        & v6_metric_1(B)
        & v7_metric_1(B)
        & v8_metric_1(B)
        & v9_metric_1(B)
        & l1_metric_1(B)
        & m1_ali2(C,B)
        & m1_subset_1(D,k1_numbers)
        & m1_subset_1(E,u1_struct_0(B))
        & m2_subset_1(F,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_5_0_ali2(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,u1_struct_0(B))
            & A = G
            & r1_xreal_0(k4_metric_1(B,G,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,G)),k4_real_1(k4_metric_1(B,E,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E)),k4_power(D,F))) ) ) ) ),
    file(ali2,a_5_0_ali2),
    [interesting(0.9),axiom,file(ali2,a_5_0_ali2)]).

fof(dh_c1_2_1__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)))))
        & ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
           => ( r2_hidden(B,A)
            <=> ? [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & B = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,C) ) ) ) )
   => ( m1_subset_1(c1_2_1__ali2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)))))
      & ! [D] : 
          ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
         => ( r2_hidden(D,c1_2_1__ali2)
          <=> ? [E] : 
                ( m2_subset_1(E,k1_numbers,k5_numbers)
                & D = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2_1__ali2),file(ali2,c1_2_1__ali2)]),
    [interesting(0.65),axiom,file(ali2,c1_2_1__ali2)]).

fof(s3_subset_1__e2_2_1__ali2,theorem,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A)
        & m1_ali2(B,A)
        & m1_subset_1(C,k1_numbers)
        & m1_subset_1(D,u1_struct_0(A)) )
     => ? [E] : 
          ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))))
          & ! [F] : 
              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
             => ( r2_hidden(F,E)
              <=> ? [G] : 
                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                    & F = a_5_0_ali2(A,B,C,D,G) ) ) ) ) ) ),
    file(ali2,s3_subset_1__e2_2_1__ali2),
    [interesting(0.9),axiom,file(ali2,s3_subset_1__e2_2_1__ali2)]).

fof(e2_2_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)))))
      & ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
         => ( r2_hidden(B,A)
          <=> ? [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & B = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,C) ) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,free_g1_pre_topc,commutativity_k3_xcmplx_0,dt_g1_pre_topc,dt_k1_funct_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_subset_1,fc4_xreal_0,rc1_xreal_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,abstractness_v1_pre_topc,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_pre_topc,dt_l1_struct_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_k5_pcomps_1,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,fc3_pcomps_1,fc4_pcomps_1,t2_tarski,fraenkel_a_5_0_ali2,s3_subset_1__e2_2_1__ali2]),
    [interesting(0.65),file(ali2,e2_2_1__ali2),[file(ali2,e2_2_1__ali2)]]).

fof(dt_c1_2_1__ali2,plain,(
    m1_subset_1(c1_2_1__ali2,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))) ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k3_xcmplx_0,abstractness_v1_pre_topc,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_xreal_0,rc1_xreal_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t2_tarski,fraenkel_a_5_0_ali2,dh_c1_2_1__ali2,e2_2_1__ali2]),
    [interesting(0.65),file(ali2,c1_2_1__ali2),[file(ali2,c1_2_1__ali2)]]).

fof(dt_c1_2_1_2__ali2,assumption,(
    m1_subset_1(c1_2_1_2__ali2,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)))) ),
    introduced(assumption,[file(ali2,c1_2_1_2__ali2)]),
    [interesting(0.5),axiom,file(ali2,c1_2_1_2__ali2)]).

fof(d2_tops_2,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v2_tops_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v4_pre_topc(C,A) ) ) ) ) ) ),
    file(tops_2,d2_tops_2),
    [interesting(0.9),axiom,file(tops_2,d2_tops_2)]).

fof(dh_c1_2_1_2__ali2,definition,
    ( ( m1_subset_1(c1_2_1_2__ali2,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
     => ~ ( r2_hidden(c1_2_1_2__ali2,c1_2_1__ali2)
          & ~ v4_pre_topc(c1_2_1_2__ali2,k5_pcomps_1(c1_2__ali2)) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
       => ~ ( r2_hidden(A,c1_2_1__ali2)
            & ~ v4_pre_topc(A,k5_pcomps_1(c1_2__ali2)) ) ) ),
    introduced(definition,[new_symbol(c1_2_1_2__ali2),file(ali2,c1_2_1_2__ali2)]),
    [interesting(0.5),axiom,file(ali2,c1_2_1_2__ali2)]).

fof(e1_2_1_2__ali2,assumption,(
    r2_hidden(c1_2_1_2__ali2,c1_2_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_2__ali2)]),
    [interesting(0.5),axiom,file(ali2,e1_2_1_2__ali2)]).

fof(involutiveness_k3_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,k3_subset_1(A,B)) = B ) ),
    file(subset_1,k3_subset_1),
    [interesting(0.9),axiom,file(subset_1,k3_subset_1)]).

fof(dt_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ),
    file(subset_1,k3_subset_1),
    [interesting(0.9),axiom,file(subset_1,k3_subset_1)]).

fof(dt_k4_pcomps_1,axiom,(
    ! [A] : 
      ( l1_metric_1(A)
     => m1_subset_1(k4_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pcomps_1,k4_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,k4_pcomps_1)]).

fof(dt_k9_metric_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_metric_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & v1_xreal_0(C) )
     => m1_subset_1(k9_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(metric_1,k9_metric_1),
    [interesting(0.9),axiom,file(metric_1,k9_metric_1)]).

fof(de_c3_2_1_2__ali2,definition,(
    c3_2_1_2__ali2 = k3_subset_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1_2__ali2) ),
    introduced(definition,[new_symbol(c3_2_1_2__ali2),file(ali2,c3_2_1_2__ali2)]),
    [interesting(0.5),axiom,file(ali2,c3_2_1_2__ali2)]).

fof(d6_pcomps_1,definition,(
    ! [A] : 
      ( l1_metric_1(A)
     => k5_pcomps_1(A) = g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A)) ) ),
    file(pcomps_1,d6_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,d6_pcomps_1)]).

fof(e4_2_1_2__ali2,plain,(
    k5_pcomps_1(c1_2__ali2) = g1_pre_topc(u1_struct_0(c1_2__ali2),k4_pcomps_1(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,dt_u1_pre_topc,cc15_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,fc1_struct_0,fc1_subset_1,fc4_pcomps_1,rc3_struct_0,t3_subset,free_g1_pre_topc,existence_l1_metric_1,dt_g1_pre_topc,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_l1_metric_1,dt_u1_struct_0,dt_c1_2__ali2,fc3_pcomps_1,d6_pcomps_1]),
    [interesting(0.5),file(ali2,e4_2_1_2__ali2),[file(ali2,e4_2_1_2__ali2)]]).

fof(e5_2_1_2__ali2,plain,(
    m1_subset_1(k3_subset_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1_2__ali2),k1_zfmisc_1(u1_struct_0(c1_2__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_u1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc15_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,free_g1_pre_topc,involutiveness_k3_subset_1,existence_m1_subset_1,dt_g1_pre_topc,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,fc1_subset_1,t3_subset,e4_2_1_2__ali2]),
    [interesting(0.5),file(ali2,e5_2_1_2__ali2),[file(ali2,e5_2_1_2__ali2)]]).

fof(dt_c3_2_1_2__ali2,plain,(
    m1_subset_1(c3_2_1_2__ali2,k1_zfmisc_1(u1_struct_0(c1_2__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,abstractness_v1_pre_topc,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc15_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,fc1_subset_1,t3_subset,de_c3_2_1_2__ali2,e5_2_1_2__ali2]),
    [interesting(0.5),file(ali2,c3_2_1_2__ali2),[file(ali2,c3_2_1_2__ali2)]]).

fof(dh_c1_2_1_2_1__ali2,definition,
    ( ( m1_subset_1(c1_2_1_2_1__ali2,u1_struct_0(c1_2__ali2))
     => ~ ( r2_hidden(c1_2_1_2_1__ali2,c3_2_1_2__ali2)
          & ! [A] : 
              ( m1_subset_1(A,k1_numbers)
             => ~ ( ~ r1_xreal_0(A,0)
                  & r1_tarski(k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,A),c3_2_1_2__ali2) ) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
       => ~ ( r2_hidden(B,c3_2_1_2__ali2)
            & ! [C] : 
                ( m1_subset_1(C,k1_numbers)
               => ~ ( ~ r1_xreal_0(C,0)
                    & r1_tarski(k9_metric_1(c1_2__ali2,B,C),c3_2_1_2__ali2) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2_1_2_1__ali2),file(ali2,c1_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c1_2_1_2_1__ali2)]).

fof(e1_2_1_2_1__ali2,assumption,(
    r2_hidden(c1_2_1_2_1__ali2,c3_2_1_2__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,e1_2_1_2_1__ali2)]).

fof(dt_c1_2_1_2_1__ali2,assumption,(
    m1_subset_1(c1_2_1_2_1__ali2,u1_struct_0(c1_2__ali2)) ),
    introduced(assumption,[file(ali2,c1_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c1_2_1_2_1__ali2)]).

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

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

fof(fc29_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B))
        & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc29_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc29_xreal_0)]).

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

fof(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_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k7_xcmplx_0(A,B))
        & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,fc6_xreal_0)]).

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

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]).

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

fof(redefinition_k5_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(real_1,k5_real_1),
    [interesting(0.9),axiom,file(real_1,k5_real_1)]).

fof(redefinition_k6_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) ),
    file(real_1,k6_real_1),
    [interesting(0.9),axiom,file(real_1,k6_real_1)]).

fof(dt_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ),
    file(real_1,k5_real_1),
    [interesting(0.9),axiom,file(real_1,k5_real_1)]).

fof(dt_k6_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ),
    file(real_1,k6_real_1),
    [interesting(0.9),axiom,file(real_1,k6_real_1)]).

fof(dh_c2_2_1_2__ali2,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & c1_2_1_2__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) )
   => ( m2_subset_1(c2_2_1_2__ali2,k1_numbers,k5_numbers)
      & c1_2_1_2__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c2_2_1_2__ali2) ) ),
    introduced(definition,[new_symbol(c2_2_1_2__ali2),file(ali2,c2_2_1_2__ali2)]),
    [interesting(0.5),axiom,file(ali2,c2_2_1_2__ali2)]).

fof(e3_2_1__ali2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
     => ( r2_hidden(A,c1_2_1__ali2)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & A = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,B) ) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k3_xcmplx_0,abstractness_v1_pre_topc,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_xreal_0,rc1_xreal_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t2_tarski,fraenkel_a_5_0_ali2,dh_c1_2_1__ali2,e2_2_1__ali2]),
    [interesting(0.65),file(ali2,e3_2_1__ali2),[file(ali2,e3_2_1__ali2)]]).

fof(e2_2_1_2__ali2,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & c1_2_1_2__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,abstractness_v1_pre_topc,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_xreal_0,fc6_membered,rc1_xreal_0,spc7_arithm,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,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_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c1_2_1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t1_subset,t3_subset,t4_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,e1_2_1_2__ali2,e3_2_1__ali2]),
    [interesting(0.5),file(ali2,e2_2_1_2__ali2),[file(ali2,e2_2_1_2__ali2)]]).

fof(dt_c2_2_1_2__ali2,plain,(
    m2_subset_1(c2_2_1_2__ali2,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1_2__ali2,e2_2_1_2__ali2]),
    [interesting(0.5),file(ali2,c2_2_1_2__ali2),[file(ali2,c2_2_1_2__ali2)]]).

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(de_c2_2_1_2_1__ali2,definition,(
    c2_2_1_2_1__ali2 = k6_real_1(k5_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_2__ali2))),2) ),
    introduced(definition,[new_symbol(c2_2_1_2_1__ali2),file(ali2,c2_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c2_2_1_2_1__ali2)]).

fof(dt_c2_2_1_2_1__ali2,plain,(
    m1_subset_1(c2_2_1_2_1__ali2,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc15_xreal_0,fc16_xreal_0,fc19_xreal_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc30_xreal_0,fc4_xreal_0,fc5_membered,fc5_xreal_0,fc6_membered,fc6_xreal_0,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,spc4_arithm,spc7_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k3_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_k5_numbers,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_struct_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,commutativity_k4_real_1,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k8_funct_2,dt_k1_numbers,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_real_1,dt_k6_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,fc2_membered,spc2_numerals,spc2_boole,de_c2_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,c2_2_1_2_1__ali2),[file(ali2,c2_2_1_2_1__ali2)]]).

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

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

fof(t6_arithm,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,1) = A ) ),
    file(arithm,t6_arithm),
    [interesting(0.9),axiom,file(arithm,t6_arithm)]).

fof(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(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(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(rqLessOrEqual__r1_xreal_0__r0_r2,theorem,(
    r1_xreal_0(0,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r3,theorem,(
    r1_xreal_0(0,3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r3)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r4,theorem,(
    r1_xreal_0(0,4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r4)]).

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__r0_rm2,theorem,(
    ~ r1_xreal_0(0,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rm3,theorem,(
    ~ r1_xreal_0(0,k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rm4,theorem,(
    ~ r1_xreal_0(0,k4_xcmplx_0(4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm4)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn1d2,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn1d3,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn1d4,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn2d3,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn3d2,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn3d4,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rn4d3,theorem,(
    r1_xreal_0(0,k7_xcmplx_0(4,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rn4d3)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rnm1d2,theorem,(
    ~ r1_xreal_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rnm1d3,theorem,(
    ~ r1_xreal_0(0,k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r0_rnm1d4,theorem,(
    ~ r1_xreal_0(0,k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r2,theorem,(
    r1_xreal_0(1,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r3,theorem,(
    r1_xreal_0(1,3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r3)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r4,theorem,(
    r1_xreal_0(1,4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r4)]).

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__r1_rm2,theorem,(
    ~ r1_xreal_0(1,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rm3,theorem,(
    ~ r1_xreal_0(1,k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rm4,theorem,(
    ~ r1_xreal_0(1,k4_xcmplx_0(4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm4)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn1d2,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn1d3,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn1d4,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn2d3,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn3d2,theorem,(
    r1_xreal_0(1,k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn3d4,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rn4d3,theorem,(
    r1_xreal_0(1,k7_xcmplx_0(4,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rn4d3)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rnm1d2,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rnm1d3,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rnm1d4,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r1_rnm3d2,theorem,(
    ~ r1_xreal_0(1,k7_xcmplx_0(k4_xcmplx_0(3),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rnm3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r1,theorem,(
    ~ r1_xreal_0(2,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r2,theorem,(
    r1_xreal_0(2,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r3,theorem,(
    r1_xreal_0(2,3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r3)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r4,theorem,(
    r1_xreal_0(2,4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r4)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rm1,theorem,(
    ~ r1_xreal_0(2,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rm2,theorem,(
    ~ r1_xreal_0(2,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rm3,theorem,(
    ~ r1_xreal_0(2,k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rm4,theorem,(
    ~ r1_xreal_0(2,k4_xcmplx_0(4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm4)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn1d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn1d3,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn1d4,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn2d3,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn3d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rn3d4,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rnm1d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rnm1d3,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r2_rnm3d2,theorem,(
    ~ r1_xreal_0(2,k7_xcmplx_0(k4_xcmplx_0(3),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rnm3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r3_r0,theorem,(
    ~ r1_xreal_0(3,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r3_r1,theorem,(
    ~ r1_xreal_0(3,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r3_r2,theorem,(
    ~ r1_xreal_0(3,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_r2)]).

fof(rqLessOrEqual__r1_xreal_0__r3_r3,theorem,(
    r1_xreal_0(3,3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_r3)]).

fof(rqLessOrEqual__r1_xreal_0__r3_r4,theorem,(
    r1_xreal_0(3,4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_r4)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rm1,theorem,(
    ~ r1_xreal_0(3,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rm2,theorem,(
    ~ r1_xreal_0(3,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rm3,theorem,(
    ~ r1_xreal_0(3,k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rm4,theorem,(
    ~ r1_xreal_0(3,k4_xcmplx_0(4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rm4)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rn1d2,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rn1d3,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rn1d4,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rn2d3,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rn3d2,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rn3d4,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rnm1d2,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r3_rnm1d3,theorem,(
    ~ r1_xreal_0(3,k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r3_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__r4_r1,theorem,(
    ~ r1_xreal_0(4,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r4_r3,theorem,(
    ~ r1_xreal_0(4,3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_r3)]).

fof(rqLessOrEqual__r1_xreal_0__r4_r4,theorem,(
    r1_xreal_0(4,4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_r4)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rm1,theorem,(
    ~ r1_xreal_0(4,k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rm2,theorem,(
    ~ r1_xreal_0(4,k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rm3,theorem,(
    ~ r1_xreal_0(4,k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rm4,theorem,(
    ~ r1_xreal_0(4,k4_xcmplx_0(4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rm4)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rn1d2,theorem,(
    ~ r1_xreal_0(4,k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rn1d4,theorem,(
    ~ r1_xreal_0(4,k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rn2d3,theorem,(
    ~ r1_xreal_0(4,k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rn3d2,theorem,(
    ~ r1_xreal_0(4,k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rn3d4,theorem,(
    ~ r1_xreal_0(4,k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__r4_rnm1d4,theorem,(
    ~ r1_xreal_0(4,k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_rnm1d4)]).

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_r2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r3,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_r4,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r4)]).

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(rqLessOrEqual__r1_xreal_0__rm1_rm2,theorem,(
    ~ r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rm3,theorem,(
    ~ r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn1d2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn1d3,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn1d4,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn2d3,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn3d2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rn3d4,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rnm1d4,theorem,(
    r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,theorem,(
    ~ r1_xreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(3),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r0,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r1,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r2,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r3,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_r4,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_rm1,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_rm2,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__rm2_rn1d4,theorem,(
    r1_xreal_0(k4_xcmplx_0(2),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_r0,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_r1,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_r2,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_r3,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_r4,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_rm1,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_rm3,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_rn1d2,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_rn1d4,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rm3_rnm3d4,theorem,(
    r1_xreal_0(k4_xcmplx_0(3),k7_xcmplx_0(k4_xcmplx_0(3),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm3_rnm3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rm4_r2,theorem,(
    r1_xreal_0(k4_xcmplx_0(4),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm4_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm4_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rm4_r4,theorem,(
    r1_xreal_0(k4_xcmplx_0(4),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm4_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm4_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rm4_rm2,theorem,(
    r1_xreal_0(k4_xcmplx_0(4),k4_xcmplx_0(2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm4_rm2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm4_rm2)]).

fof(rqLessOrEqual__r1_xreal_0__rm4_rm4,theorem,(
    r1_xreal_0(k4_xcmplx_0(4),k4_xcmplx_0(4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rm4_rm4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm4_rm4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rm3,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn1d4,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rn3d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,3),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,3),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,3),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,3),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,3),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,3),k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,3),k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,4),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_rm3,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,4),k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_rn1d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_rn3d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(1,4),k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_rnm1d4,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn1d4_rnm3d4,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(3),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn1d4_rnm3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(2,3),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(2,3),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(2,3),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(2,3),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(2,3),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(2,3),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(2,3),k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,theorem,(
    r1_xreal_0(k7_xcmplx_0(2,3),k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_r1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,2),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,2),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,2),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,2),k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_rn3d4,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,2),k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_r0,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,4),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,4),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,4),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,4),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,4),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,4),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_rn1d2,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,4),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_rn1d4,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,4),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_rn3d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,4),k7_xcmplx_0(3,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d2)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_rn3d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(3,4),k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rn3d4_rnm1d4,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(3,4),k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rn3d4_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r0,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_r0,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(1,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(2,3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(k4_xcmplx_0(1),3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_r0,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_r2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_rm1,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k4_xcmplx_0(1)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rm1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d2,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(1,2)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d2)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_rn3d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(3,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rn3d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm1d4_rnm1d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(k4_xcmplx_0(1),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm1d4_rnm1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_r0,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r0)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_r1,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r1)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_r3,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),3) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_r4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),4) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_r4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_rm3,theorem,(
    ~ r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k4_xcmplx_0(3)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_rm3),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_rm3)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_rn1d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(1,4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_rn1d4)]).

fof(rqLessOrEqual__r1_xreal_0__rnm3d4_rnm3d4,theorem,(
    r1_xreal_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(k4_xcmplx_0(3),4)) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rnm3d4_rnm3d4)]).

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_r3_rm3,theorem,(
    k6_xcmplx_0(0,3) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r3_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r3_rm3)]).

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__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__r0_rm3_r3,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(3)) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm3_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm3_r3)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rm4_r4,theorem,(
    k6_xcmplx_0(0,k4_xcmplx_0(4)) = 4 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm4_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm4_r4)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn1d4_rnm1d4,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d4_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(3,2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rn3d4_rnm3d4,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(3,4)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn3d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn3d4_rnm3d4)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d4_rn1d4,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d4_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3,theorem,(
    k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3)]).

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

fof(rqRealDiff__k6_xcmplx_0__r1_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_r3_rm2,theorem,(
    k6_xcmplx_0(1,3) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r3_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_r4_rm3,theorem,(
    k6_xcmplx_0(1,4) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_r4_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r4_rm3)]).

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__r1_rm2_r3,theorem,(
    k6_xcmplx_0(1,k4_xcmplx_0(2)) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm2_r3)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rm3_r4,theorem,(
    k6_xcmplx_0(1,k4_xcmplx_0(3)) = 4 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm3_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm3_r4)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(1,3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn1d4_rn3d4,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(1,4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d4_rn3d4)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(2,3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(3,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn3d4_rn1d4,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(3,4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn3d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn3d4_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn4d3_rnm1d3,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(4,3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn4d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn4d3_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rnm1d3_rn4d3,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rnm1d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rnm1d3_rn4d3)]).

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__r2_r3_rm1,theorem,(
    k6_xcmplx_0(2,3) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r3_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r2_rm1_r3,theorem,(
    k6_xcmplx_0(2,k4_xcmplx_0(1)) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_rm1_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rm1_r3)]).

fof(rqRealDiff__k6_xcmplx_0__r2_rm2_r4,theorem,(
    k6_xcmplx_0(2,k4_xcmplx_0(2)) = 4 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_rm2_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rm2_r4)]).

fof(rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2,theorem,(
    k6_xcmplx_0(2,k7_xcmplx_0(1,2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_rn2d3_rn4d3,theorem,(
    k6_xcmplx_0(2,k7_xcmplx_0(2,3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn2d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn2d3_rn4d3)]).

fof(rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2,theorem,(
    k6_xcmplx_0(2,k7_xcmplx_0(3,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r2_rn4d3_rn2d3,theorem,(
    k6_xcmplx_0(2,k7_xcmplx_0(4,3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn4d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_rn4d3_rn2d3)]).

fof(rqRealDiff__k6_xcmplx_0__r3_r0_r3,theorem,(
    k6_xcmplx_0(3,0) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_r0_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r0_r3)]).

fof(rqRealDiff__k6_xcmplx_0__r3_r1_r2,theorem,(
    k6_xcmplx_0(3,1) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r1_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r3_r2_r1,theorem,(
    k6_xcmplx_0(3,2) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r3_r3_r0,theorem,(
    k6_xcmplx_0(3,3) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_r3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__r3_r4_rm1,theorem,(
    k6_xcmplx_0(3,4) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_r4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_r4_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__r3_rm1_r4,theorem,(
    k6_xcmplx_0(3,k4_xcmplx_0(1)) = 4 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_rm1_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_rm1_r4)]).

fof(rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2,theorem,(
    k6_xcmplx_0(3,k7_xcmplx_0(3,2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2)]).

fof(rqRealDiff__k6_xcmplx_0__r4_r0_r4,theorem,(
    k6_xcmplx_0(4,0) = 4 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r4_r0_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r4_r0_r4)]).

fof(rqRealDiff__k6_xcmplx_0__r4_r1_r3,theorem,(
    k6_xcmplx_0(4,1) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r4_r1_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r4_r1_r3)]).

fof(rqRealDiff__k6_xcmplx_0__r4_r2_r2,theorem,(
    k6_xcmplx_0(4,2) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r4_r2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r4_r2_r2)]).

fof(rqRealDiff__k6_xcmplx_0__r4_r3_r1,theorem,(
    k6_xcmplx_0(4,3) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r4_r3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r4_r3_r1)]).

fof(rqRealDiff__k6_xcmplx_0__r4_r4_r0,theorem,(
    k6_xcmplx_0(4,4) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r4_r4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r4_r4_r0)]).

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

fof(rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),2) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_r3_rm4,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),3) = k4_xcmplx_0(4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r3_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r3_rm4)]).

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(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__rm1_rm3_r2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(3)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rm4_r3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(4)) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm4_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm4_r3)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rn1d3_rnm4d3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rn1d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rn1d3_rnm4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d4_rnm3d4,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d4_rnm3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm3d4_rnm1d4,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm3d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm3d4_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm4d3_rn1d3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(4),3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm4d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm4d3_rn1d3)]).

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_r1_rm3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_r2_rm4,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),2) = k4_xcmplx_0(4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r2_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r2_rm4)]).

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(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(rqRealDiff__k6_xcmplx_0__rm2_rm3_r1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(3)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rm4_r2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(4)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm4_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm4_r2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rnm2d3_rnm4d3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm2d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm2d3_rnm4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rm2_rnm4d3_rnm2d3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(4),3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm4d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rnm4d3_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),0) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_r1_rm4,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),1) = k4_xcmplx_0(4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_r1_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_r1_rm4)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_rm4_r1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(4)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rm4_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rm4_r0_rm4,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(4),0) = k4_xcmplx_0(4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm4_r0_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm4_r0_rm4)]).

fof(rqRealDiff__k6_xcmplx_0__rm4_rm1_rm3,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(4),k4_xcmplx_0(1)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm1_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm1_rm3)]).

fof(rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(4),k4_xcmplx_0(2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rm4_rm3_rm1,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(4),k4_xcmplx_0(3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm3_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rm4_rm4_r0,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(4),k4_xcmplx_0(4)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm4_rm4_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),2) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d4_rn1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d4_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn3d4_rnm1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(3,4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d4_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d4_rn3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d4_rn3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),0) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),1) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_rm1_rn4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),k4_xcmplx_0(1)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rm1_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rm1_rn4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(1,3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_rn4d3_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(4,3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rn4d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rn4d3_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_r0_rn1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),0) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_r0_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_r0_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_r1_rnm3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),1) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_r1_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_r1_rnm3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_rn1d2_rnm1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rn1d2_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rn1d2_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_rn1d4_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(1,4)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rn1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rn1d4_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_rn3d4_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(3,4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rn3d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rn3d4_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_rnm1d2_rn3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rnm1d2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rnm1d2_rn3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_rnm1d4_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rnm1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rnm1d4_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn1d4_rnm3d4_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(3),4)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rnm3d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d4_rnm3d4_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),0) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),1) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_r2_rnm4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),2) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_r2_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_r2_rnm4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(1,3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(2,3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_rn4d3_rnm2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(4,3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rn4d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rn4d3_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_rnm2d3_rn4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rnm2d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rnm2d3_rn4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn2d3_rnm4d3_r2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(4),3)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rnm4d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn2d3_rnm4d3_r2)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),1) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),3) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(1,2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(3,2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_rn3d4_rn3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(3,4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d4_rn3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 3 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d4_r0_rn3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,4),0) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_r0_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_r0_rn3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d4_r1_rnm1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,4),1) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_r1_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_r1_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d4_rn1d2_rn1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rn1d2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rn1d2_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d4_rn1d4_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rn1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rn1d4_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d4_rn3d4_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(3,4)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rn3d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rn3d4_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn3d4_rnm1d4_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rnm1d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn3d4_rnm1d4_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn4d3_r0_rn4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(4,3),0) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_r0_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_r0_rn4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn4d3_r1_rn1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(4,3),1) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_r1_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_r1_rn1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn4d3_r2_rnm2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(4,3),2) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_r2_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_r2_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rn4d3_rn1d3_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(1,3)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_rn1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_rn1d3_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rn4d3_rn4d3_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(4,3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_rn4d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_rn4d3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rn4d3_rnm2d3_r2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = 2 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_rnm2d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn4d3_rnm2d3_r2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d4_rnm3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d4_rnm3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(3,2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d4_rnm1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d4_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 1 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d4_rn1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d4_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),0) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_r1_rnm4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),1) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_r1_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_r1_rnm4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k4_xcmplx_0(1)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(2,3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_r0_rnm1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),0) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_r0_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_r0_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rm1_rn3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k4_xcmplx_0(1)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rm1_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rm1_rn3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rn1d2_rnm3d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rn1d2_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rn1d2_rnm3d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rn1d4_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rn1d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rn1d4_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rn3d4_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(3,4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rn3d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rn3d4_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rnm1d2_rn1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rnm1d2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rnm1d2_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rnm1d4_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rnm1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rnm1d4_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d4_rnm3d4_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rnm3d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d4_rnm3d4_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k4_xcmplx_0(1)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rm2_rn4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k4_xcmplx_0(2)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rm2_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rm2_rn4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(1,3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rn2d3_rnm4d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rn2d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rn2d3_rnm4d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rn4d3_rm2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(4,3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rn4d3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rn4d3_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k4_xcmplx_0(2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k4_xcmplx_0(3)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(3,2)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d4_rm1_rn1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k4_xcmplx_0(1)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rm1_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rm1_rn1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d4_rn1d4_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(1,4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rn1d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rn1d4_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d4_rnm1d2_rnm1d4,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rnm1d2_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rnm1d2_rnm1d4)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d4_rnm1d4_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rnm1d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rnm1d4_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm3d4_rnm3d4_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(k4_xcmplx_0(3),4)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rnm3d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm3d4_rnm3d4_r0)]).

fof(rqRealDiff__k6_xcmplx_0__rnm4d3_rm2_rn2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k4_xcmplx_0(2)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rm2_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rm2_rn2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm4d3_rn2d3_rm2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(2,3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rn2d3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rn2d3_rm2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm4d3_rnm1d3_rm1,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rnm1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rnm1d3_rm1)]).

fof(rqRealDiff__k6_xcmplx_0__rnm4d3_rnm2d3_rnm2d3,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rnm2d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rnm2d3_rnm2d3)]).

fof(rqRealDiff__k6_xcmplx_0__rnm4d3_rnm4d3_r0,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(4),3)) = 0 ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rnm4d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm4d3_rnm4d3_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,(
    k7_xcmplx_0(0,1) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,(
    k7_xcmplx_0(0,2) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r3_r0,theorem,(
    k7_xcmplx_0(0,3) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r3_r0)]).

fof(rqRealDiv__k7_xcmplx_0__r0_r4_r0,theorem,(
    k7_xcmplx_0(0,4) = 0 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r0_r4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r4_r0)]).

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

fof(rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3,theorem,(
    k7_xcmplx_0(1,3) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r4_rn1d4,theorem,(
    k7_xcmplx_0(1,4) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r4_rn1d4)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rm4_rnm1d4,theorem,(
    k7_xcmplx_0(1,k4_xcmplx_0(4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm4_rnm1d4)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(1,3)) = 3 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn1d4_r4,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(1,4)) = 4 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d4_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d4_r4)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(3,2)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rn3d4_rn4d3,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(3,4)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn3d4_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn3d4_rn4d3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d4_rm4,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k4_xcmplx_0(4) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d4_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d4_rm4)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm3d4_rnm4d3,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm3d4_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm3d4_rnm4d3)]).

fof(rqRealDiv__k7_xcmplx_0__r1_rnm4d3_rnm3d4,theorem,(
    k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(4),3)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm4d3_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm4d3_rnm3d4)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,(
    k7_xcmplx_0(2,1) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,(
    k7_xcmplx_0(2,2) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]).

fof(rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3,theorem,(
    k7_xcmplx_0(2,3) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3)]).

fof(rqRealDiv__k7_xcmplx_0__r2_rn1d2_r4,theorem,(
    k7_xcmplx_0(2,k7_xcmplx_0(1,2)) = 4 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r2_rn1d2_r4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_rn1d2_r4)]).

fof(rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2,theorem,(
    k7_xcmplx_0(3,2) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2)]).

fof(rqRealDiv__k7_xcmplx_0__r3_r3_r1,theorem,(
    k7_xcmplx_0(3,3) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r3_r3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r3_r3_r1)]).

fof(rqRealDiv__k7_xcmplx_0__r3_r4_rn3d4,theorem,(
    k7_xcmplx_0(3,4) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r3_r4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r3_r4_rn3d4)]).

fof(rqRealDiv__k7_xcmplx_0__r4_r2_r2,theorem,(
    k7_xcmplx_0(4,2) = 2 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r4_r2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r4_r2_r2)]).

fof(rqRealDiv__k7_xcmplx_0__r4_r3_rn4d3,theorem,(
    k7_xcmplx_0(4,3) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r4_r3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r4_r3_rn4d3)]).

fof(rqRealDiv__k7_xcmplx_0__r4_r4_r1,theorem,(
    k7_xcmplx_0(4,4) = 1 ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r4_r4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r4_r4_r1)]).

fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,(
    k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]).

fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,theorem,(
    k7_xcmplx_0(k4_xcmplx_0(1),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]).

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_r3_r0,theorem,(
    k3_xcmplx_0(0,3) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r3_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_r4_r0,theorem,(
    k3_xcmplx_0(0,4) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_r4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r4_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__r0_rm3_r0,theorem,(
    k3_xcmplx_0(0,k4_xcmplx_0(3)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rm3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm3_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,theorem,(
    k3_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_rn1d3_r0,theorem,(
    k3_xcmplx_0(0,k7_xcmplx_0(1,3)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_rn1d4_r0,theorem,(
    k3_xcmplx_0(0,k7_xcmplx_0(1,4)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d4_r0)]).

fof(rqRealMult__k3_xcmplx_0__r0_rn3d2_r0,theorem,(
    k3_xcmplx_0(0,k7_xcmplx_0(3,2)) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r0_rn3d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn3d2_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_r3_r3,theorem,(
    k3_xcmplx_0(1,3) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r3_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r3_r3)]).

fof(rqRealMult__k3_xcmplx_0__r1_r4_r4,theorem,(
    k3_xcmplx_0(1,4) = 4 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_r4_r4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r4_r4)]).

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__r1_rm3_rm3,theorem,(
    k3_xcmplx_0(1,k4_xcmplx_0(3)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rm3_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm3_rm3)]).

fof(rqRealMult__k3_xcmplx_0__r1_rm4_rm4,theorem,(
    k3_xcmplx_0(1,k4_xcmplx_0(4)) = k4_xcmplx_0(4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rm4_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm4_rm4)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(1,3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn1d4_rn1d4,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d4_rn1d4)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(2,3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(3,2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__r1_rn3d4_rn3d4,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(3,4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rn3d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn3d4_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__r1_rnm1d4_rnm1d4,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d4_rnm1d4)]).

fof(rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3,theorem,(
    k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3)]).

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__r2_r2_r4,theorem,(
    k3_xcmplx_0(2,2) = 4 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_r2_r4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r2_r4)]).

fof(rqRealMult__k3_xcmplx_0__r2_rm2_rm4,theorem,(
    k3_xcmplx_0(2,k4_xcmplx_0(2)) = k4_xcmplx_0(4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rm2_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rm2_rm4)]).

fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(1,2)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]).

fof(rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(1,3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__r2_rn1d4_rn1d2,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d4_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__r2_rn2d3_rn4d3,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(2,3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn2d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn2d3_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__r2_rn3d2_r3,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(3,2)) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3)]).

fof(rqRealMult__k3_xcmplx_0__r2_rn3d4_rn3d2,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(3,4)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rn3d4_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn3d4_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)]).

fof(rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3)]).

fof(rqRealMult__k3_xcmplx_0__r2_rnm1d4_rnm1d2,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d4_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__r2_rnm2d3_rnm4d3,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm2d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm2d3_rnm4d3)]).

fof(rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(3),2)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3)]).

fof(rqRealMult__k3_xcmplx_0__r2_rnm3d4_rnm3d2,theorem,(
    k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm3d4_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm3d4_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__r3_r0_r0,theorem,(
    k3_xcmplx_0(3,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r3_r1_r3,theorem,(
    k3_xcmplx_0(3,1) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_r1_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_r1_r3)]).

fof(rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(1,2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__r3_rn1d3_r1,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(1,3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1)]).

fof(rqRealMult__k3_xcmplx_0__r3_rn1d4_rn3d4,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(1,4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rn1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rn1d4_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__r3_rn2d3_r2,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(2,3)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2)]).

fof(rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__r3_rnm1d4_rnm3d4,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm1d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm1d4_rnm3d4)]).

fof(rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2,theorem,(
    k3_xcmplx_0(3,k7_xcmplx_0(k4_xcmplx_0(2),3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2)]).

fof(rqRealMult__k3_xcmplx_0__r4_r0_r0,theorem,(
    k3_xcmplx_0(4,0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__r4_r1_r4,theorem,(
    k3_xcmplx_0(4,1) = 4 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_r1_r4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_r1_r4)]).

fof(rqRealMult__k3_xcmplx_0__r4_rn1d2_r2,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(1,2)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rn1d2_r2)]).

fof(rqRealMult__k3_xcmplx_0__r4_rn1d3_rn4d3,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(1,3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rn1d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rn1d3_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__r4_rn1d4_r1,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(1,4)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rn1d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rn1d4_r1)]).

fof(rqRealMult__k3_xcmplx_0__r4_rn3d4_r3,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(3,4)) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rn3d4_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rn3d4_r3)]).

fof(rqRealMult__k3_xcmplx_0__r4_rnm1d2_rm2,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm1d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm1d2_rm2)]).

fof(rqRealMult__k3_xcmplx_0__r4_rnm1d3_rnm4d3,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm1d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm1d3_rnm4d3)]).

fof(rqRealMult__k3_xcmplx_0__r4_rnm1d4_rm1,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm1d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm1d4_rm1)]).

fof(rqRealMult__k3_xcmplx_0__r4_rnm3d4_rm3,theorem,(
    k3_xcmplx_0(4,k7_xcmplx_0(k4_xcmplx_0(3),4)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm3d4_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r4_rnm3d4_rm3)]).

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(rqRealMult__k3_xcmplx_0__rm2_r2_rm4,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),2) = k4_xcmplx_0(4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_r2_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r2_rm4)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rm2_r4,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 4 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rm2_r4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rm2_r4)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rn1d4_rnm1d2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d4_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rn2d3_rnm4d3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn2d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn2d3_rnm4d3)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(3,2)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d4_rn1d2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d4_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rnm2d3_rn4d3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm2d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm2d3_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3)]).

fof(rqRealMult__k3_xcmplx_0__rm3_r0_r0,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__rm3_r1_rm3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),1) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_r1_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_r1_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(1,3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rn1d4_rnm3d4,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn1d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn1d4_rnm3d4)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(2,3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rnm1d4_rn3d4,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm1d4_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2)]).

fof(rqRealMult__k3_xcmplx_0__rm4_r1_rm4,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),1) = k4_xcmplx_0(4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_r1_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_r1_rm4)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rn1d2_rm2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(1,2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn1d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn1d2_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rn1d3_rnm4d3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn1d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn1d3_rnm4d3)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rn1d4_rm1,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(1,4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn1d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn1d4_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rn3d4_rm3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(3,4)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn3d4_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rn3d4_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rnm1d2_r2,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm1d2_r2)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rnm1d3_rn4d3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm1d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm1d3_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rnm1d4_r1,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm1d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm1d4_r1)]).

fof(rqRealMult__k3_xcmplx_0__rm4_rnm3d4_r3,theorem,(
    k3_xcmplx_0(k4_xcmplx_0(4),k7_xcmplx_0(k4_xcmplx_0(3),4)) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm3d4_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm4_rnm3d4_r3)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),2) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),3) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r4_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),4) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r4_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r4_r2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(3)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_rm4_rm2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(4)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm4_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm4_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_rn1d2_rn1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rn1d2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rn1d2_rn1d4)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_rn3d2_rn3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rn3d2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rn3d2_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_rnm1d2_rnm1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rnm1d2_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rnm1d2_rnm1d4)]).

fof(rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,3),1) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3)]).

fof(rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,3),2) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,3),3) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn1d3_r4_rn4d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,3),4) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r4_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_r4_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,3),k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3)]).

fof(rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,3),k4_xcmplx_0(3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_r0_r0,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_r1_rn1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),1) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r1_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r1_rn1d4)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_r2_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),2) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r2_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_r3_rn3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),3) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r3_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r3_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_r4_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),4) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_r4_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_rm2_rnm1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_rm2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_rm2_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_rm3_rnm3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),k4_xcmplx_0(3)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_rm3_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_rm3_rnm3d4)]).

fof(rqRealMult__k3_xcmplx_0__rn1d4_rm4_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,4),k4_xcmplx_0(4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_rm4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d4_rm4_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),1) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_r2_rn4d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),2) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_r2_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_r2_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),3) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),k4_xcmplx_0(3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(3,2)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),0) = 0 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),1) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),2) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k4_xcmplx_0(2)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(1,3)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(2,3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rn4d3_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(4,3)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rn4d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rn4d3_r2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rn3d2_rnm4d3_rm2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(4),3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rnm4d3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d2_rnm4d3_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_r1_rn3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),1) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_r1_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_r1_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_r2_rn3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),2) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_r2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_r2_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_r4_r3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),4) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_r4_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_r4_r3)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_rm2_rnm3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rm2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rm2_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_rm4_rm3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),k4_xcmplx_0(4)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rm4_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rm4_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_rn4d3_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(4,3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rn4d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rn4d3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn3d4_rnm4d3_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(k4_xcmplx_0(4),3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rnm4d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn3d4_rnm4d3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rn4d3_r1_rn4d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(4,3),1) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_r1_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_r1_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__rn4d3_r3_r4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(4,3),3) = 4 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_r3_r4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_r3_r4)]).

fof(rqRealMult__k3_xcmplx_0__rn4d3_rn1d4_rn1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rn1d4_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rn1d4_rn1d3)]).

fof(rqRealMult__k3_xcmplx_0__rn4d3_rn3d4_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(3,4)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rn3d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rn3d4_r1)]).

fof(rqRealMult__k3_xcmplx_0__rn4d3_rnm1d4_rnm1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rnm1d4_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rnm1d4_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__rn4d3_rnm3d4_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(k4_xcmplx_0(3),4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rnm3d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn4d3_rnm3d4_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),3) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_r4_rm2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),4) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r4_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r4_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(2)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(3)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm4_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(4)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm4_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm4_r2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_rn1d2_rnm1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rn1d2_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rn1d2_rnm1d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_rnm1d2_rn1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rnm1d2_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rnm1d2_rn1d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),1) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),2) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),3) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k4_xcmplx_0(2)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k4_xcmplx_0(3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_r1_rnm1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),1) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r1_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r1_rnm1d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_r2_rnm1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r2_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_r3_rnm3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),3) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r3_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r3_rnm3d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_r4_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),4) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_r4_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_rm2_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k4_xcmplx_0(2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_rm2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_rm2_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_rm3_rn3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k4_xcmplx_0(3)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_rm3_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_rm3_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d4_rm4_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k4_xcmplx_0(4)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_rm4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d4_rm4_r1)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),1) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_r2_rnm4d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),2) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_r2_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_r2_rnm4d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),3) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_rm2_rn4d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k4_xcmplx_0(2)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rm2_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rm2_rn4d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k4_xcmplx_0(3)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),1) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),2) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k4_xcmplx_0(2)) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rn1d2_rnm3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rn1d2_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rn1d2_rnm3d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(2,3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rn4d3_rm2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(4,3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rn4d3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rn4d3_rm2)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d2_rn3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d2_rn3d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(k4_xcmplx_0(2),3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d2_rnm4d3_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(k4_xcmplx_0(4),3)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm4d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d2_rnm4d3_r2)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_r1_rnm3d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),1) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_r1_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_r1_rnm3d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_r2_rnm3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),2) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_r2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_r2_rnm3d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_r4_rm3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),4) = k4_xcmplx_0(3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_r4_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_r4_rm3)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_rm2_rn3d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k4_xcmplx_0(2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rm2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rm2_rn3d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_rm4_r3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k4_xcmplx_0(4)) = 3 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rm4_r3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rm4_r3)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_rn1d3_rnm1d4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rn1d3_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rn1d3_rnm1d4)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_rn4d3_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(4,3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rn4d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rn4d3_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm3d4_rnm4d3_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(k4_xcmplx_0(4),3)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rnm4d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm3d4_rnm4d3_r1)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_r1_rnm4d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),1) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_r1_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_r1_rnm4d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_r3_rm4,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),3) = k4_xcmplx_0(4) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_r3_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_r3_rm4)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rn1d2_rnm2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d2_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d2_rnm2d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rn1d4_rnm1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d4_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d4_rnm1d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rn3d4_rm1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(3,4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rn3d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rn3d4_rm1)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d2_rn2d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d2_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d2_rn2d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d4_rn1d3,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d4_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d4_rn1d3)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d2_r2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 2 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d2_r2)]).

fof(rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d4_r1,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3),k7_xcmplx_0(k4_xcmplx_0(3),4)) = 1 ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d4_r1)]).

fof(rqRealNeg__k4_xcmplx_0__r3_rm3,theorem,(
    k4_xcmplx_0(3) = k4_xcmplx_0(3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r3_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r3_rm3)]).

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(rqRealNeg__k4_xcmplx_0__rm3_r3,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(3)) = 3 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm3_r3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm3_r3)]).

fof(rqRealNeg__k4_xcmplx_0__rm4_r4,theorem,(
    k4_xcmplx_0(k4_xcmplx_0(4)) = 4 ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rm4_r4),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm4_r4)]).

fof(rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(1,3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3)]).

fof(rqRealNeg__k4_xcmplx_0__rn1d4_rnm1d4,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d4_rnm1d4)]).

fof(rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3)]).

fof(rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(3,2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2)]).

fof(rqRealNeg__k4_xcmplx_0__rn3d4_rnm3d4,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(3,4)) = k7_xcmplx_0(k4_xcmplx_0(3),4) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn3d4_rnm3d4),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn3d4_rnm3d4)]).

fof(rqRealNeg__k4_xcmplx_0__rn4d3_rnm4d3,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(4,3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn4d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn4d3_rnm4d3)]).

fof(rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3)]).

fof(rqRealNeg__k4_xcmplx_0__rnm1d4_rn1d4,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d4_rn1d4)]).

fof(rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3)]).

fof(rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2)]).

fof(rqRealNeg__k4_xcmplx_0__rnm3d4_rn3d4,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm3d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm3d4_rn3d4)]).

fof(rqRealNeg__k4_xcmplx_0__rnm4d3_rn4d3,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(4),3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm4d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm4d3_rn4d3)]).

fof(spc3_numerals,theorem,
    ( v2_xreal_0(3)
    & m2_subset_1(3,k1_numbers,k5_numbers)
    & m1_subset_1(3,k5_numbers)
    & m1_subset_1(3,k1_numbers) ),
    file(numerals,spc3_numerals),
    [interesting(0.9),axiom,file(numerals,spc3_numerals)]).

fof(spc4_numerals,theorem,
    ( v2_xreal_0(4)
    & m2_subset_1(4,k1_numbers,k5_numbers)
    & m1_subset_1(4,k5_numbers)
    & m1_subset_1(4,k1_numbers) ),
    file(numerals,spc4_numerals),
    [interesting(0.9),axiom,file(numerals,spc4_numerals)]).

fof(spc3_boole,theorem,(
    ~ v1_xboole_0(3) ),
    file(boole,spc3_boole),
    [interesting(0.9),axiom,file(boole,spc3_boole)]).

fof(spc4_boole,theorem,(
    ~ v1_xboole_0(4) ),
    file(boole,spc4_boole),
    [interesting(0.9),axiom,file(boole,spc4_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(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__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(t54_subset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(A))
     => ~ ( r2_hidden(B,k3_subset_1(A,C))
          & r2_hidden(B,C) ) ) ),
    file(subset_1,t54_subset_1),
    [interesting(0.9),axiom,file(subset_1,t54_subset_1)]).

fof(e3_2_1_2_1__ali2,plain,(
    ~ r2_hidden(c1_2_1_2_1__ali2,c1_2_1_2__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,dt_c1_2__ali2,e1_2_1_2_1__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,abstractness_v1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_xboole_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc6_membered,rc1_membered,rc3_struct_0,rc5_struct_0,reflexivity_r1_tarski,dt_k5_pcomps_1,dt_u1_struct_0,dt_c1_2__ali2,cc15_membered,rc1_subset_1,rc2_subset_1,t2_subset,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_m1_subset_1,dt_c1_2_1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c3_2_1_2__ali2,de_c3_2_1_2__ali2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_2_1_2_1__ali2,t54_subset_1]),
    [interesting(0.35),file(ali2,e3_2_1_2_1__ali2),[file(ali2,e3_2_1_2_1__ali2)]]).

fof(e3_2_1_2__ali2,plain,(
    c1_2_1_2__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c2_2_1_2__ali2) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1_2__ali2,e2_2_1_2__ali2]),
    [interesting(0.5),file(ali2,e3_2_1_2__ali2),[file(ali2,e3_2_1_2__ali2)]]).

fof(e4_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_2__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,e1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc1_xreal_0,fc4_subset_1,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_l1_pre_topc,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_k5_pcomps_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc2_membered,fc3_pcomps_1,fc4_pcomps_1,fc4_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e3_2_1_2_1__ali2,e3_2_1_2__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e4_2_1_2_1__ali2),[file(ali2,e4_2_1_2_1__ali2)]]).

fof(t52_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & r1_xreal_0(k6_xcmplx_0(B,A),0) ) ) ) ),
    file(xreal_1,t52_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t52_xreal_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(e5_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(k5_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_2__ali2))),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,e1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_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,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_real_1,dt_k6_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__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,e4_2_1_2_1__ali2,t52_xreal_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e5_2_1_2_1__ali2),[file(ali2,e5_2_1_2_1__ali2)]]).

fof(t3_seq_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(A,0)
       => ( ~ r1_xreal_0(k7_xcmplx_0(A,2),0)
          & ~ r1_xreal_0(k7_xcmplx_0(A,4),0) ) ) ) ),
    file(seq_2,t3_seq_2),
    [interesting(0.9),axiom,file(seq_2,t3_seq_2)]).

fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,(
    k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]).

fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]).

fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]).

fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,theorem,(
    k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)]).

fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,theorem,(
    k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]).

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__r4_rm4,theorem,(
    k4_xcmplx_0(4) = k4_xcmplx_0(4) ),
    file(arithm,rqRealNeg__k4_xcmplx_0__r4_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r4_rm4)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,theorem,(
    k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,theorem,(
    k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2)]).

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_r4_rm4,theorem,(
    k6_xcmplx_0(0,4) = k4_xcmplx_0(4) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r0_r4_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r4_rm4)]).

fof(rqRealDiff__k6_xcmplx_0__r2_r4_rm2,theorem,(
    k6_xcmplx_0(2,4) = k4_xcmplx_0(2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__r2_r4_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r4_rm2)]).

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__rn1d2_r1_rnm1d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]).

fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,theorem,(
    k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2)]).

fof(rqLessOrEqual__r1_xreal_0__r2_r0,theorem,(
    ~ r1_xreal_0(2,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r4_r0,theorem,(
    ~ r1_xreal_0(4,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r4_r2,theorem,(
    ~ r1_xreal_0(4,2) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r4_r2),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r4_r2)]).

fof(e6_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(c2_2_1_2_1__ali2,0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,e1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k6_real_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_k6_real_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc30_xreal_0,rc1_xreal_0,rc3_struct_0,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_real_1,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,de_c2_2_1_2_1__ali2,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r3,rqLessOrEqual__r1_xreal_0__r0_r4,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm3,rqLessOrEqual__r1_xreal_0__r0_rm4,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rn1d3,rqLessOrEqual__r1_xreal_0__r0_rn1d4,rqLessOrEqual__r1_xreal_0__r0_rn2d3,rqLessOrEqual__r1_xreal_0__r0_rn3d2,rqLessOrEqual__r1_xreal_0__r0_rn3d4,rqLessOrEqual__r1_xreal_0__r0_rn4d3,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d3,rqLessOrEqual__r1_xreal_0__r0_rnm1d4,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r3,rqLessOrEqual__r1_xreal_0__r1_r4,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm3,rqLessOrEqual__r1_xreal_0__r1_rm4,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rn1d3,rqLessOrEqual__r1_xreal_0__r1_rn1d4,rqLessOrEqual__r1_xreal_0__r1_rn2d3,rqLessOrEqual__r1_xreal_0__r1_rn3d2,rqLessOrEqual__r1_xreal_0__r1_rn3d4,rqLessOrEqual__r1_xreal_0__r1_rn4d3,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_rnm1d4,rqLessOrEqual__r1_xreal_0__r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r2_r3,rqLessOrEqual__r1_xreal_0__r2_r4,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm3,rqLessOrEqual__r1_xreal_0__r2_rm4,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rn1d3,rqLessOrEqual__r1_xreal_0__r2_rn1d4,rqLessOrEqual__r1_xreal_0__r2_rn2d3,rqLessOrEqual__r1_xreal_0__r2_rn3d2,rqLessOrEqual__r1_xreal_0__r2_rn3d4,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d3,rqLessOrEqual__r1_xreal_0__r2_rnm3d2,rqLessOrEqual__r1_xreal_0__r3_r0,rqLessOrEqual__r1_xreal_0__r3_r1,rqLessOrEqual__r1_xreal_0__r3_r2,rqLessOrEqual__r1_xreal_0__r3_r3,rqLessOrEqual__r1_xreal_0__r3_r4,rqLessOrEqual__r1_xreal_0__r3_rm1,rqLessOrEqual__r1_xreal_0__r3_rm2,rqLessOrEqual__r1_xreal_0__r3_rm3,rqLessOrEqual__r1_xreal_0__r3_rm4,rqLessOrEqual__r1_xreal_0__r3_rn1d2,rqLessOrEqual__r1_xreal_0__r3_rn1d3,rqLessOrEqual__r1_xreal_0__r3_rn1d4,rqLessOrEqual__r1_xreal_0__r3_rn2d3,rqLessOrEqual__r1_xreal_0__r3_rn3d2,rqLessOrEqual__r1_xreal_0__r3_rn3d4,rqLessOrEqual__r1_xreal_0__r3_rnm1d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d3,rqLessOrEqual__r1_xreal_0__r4_r1,rqLessOrEqual__r1_xreal_0__r4_r3,rqLessOrEqual__r1_xreal_0__r4_r4,rqLessOrEqual__r1_xreal_0__r4_rm1,rqLessOrEqual__r1_xreal_0__r4_rm2,rqLessOrEqual__r1_xreal_0__r4_rm3,rqLessOrEqual__r1_xreal_0__r4_rm4,rqLessOrEqual__r1_xreal_0__r4_rn1d2,rqLessOrEqual__r1_xreal_0__r4_rn1d4,rqLessOrEqual__r1_xreal_0__r4_rn2d3,rqLessOrEqual__r1_xreal_0__r4_rn3d2,rqLessOrEqual__r1_xreal_0__r4_rn3d4,rqLessOrEqual__r1_xreal_0__r4_rnm1d4,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r3,rqLessOrEqual__r1_xreal_0__rm1_r4,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rm3,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rn1d3,rqLessOrEqual__r1_xreal_0__rm1_rn1d4,rqLessOrEqual__r1_xreal_0__rm1_rn2d3,rqLessOrEqual__r1_xreal_0__rm1_rn3d2,rqLessOrEqual__r1_xreal_0__rm1_rn3d4,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_rnm1d4,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r3,rqLessOrEqual__r1_xreal_0__rm2_r4,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm2_rn1d4,rqLessOrEqual__r1_xreal_0__rm3_r0,rqLessOrEqual__r1_xreal_0__rm3_r1,rqLessOrEqual__r1_xreal_0__rm3_r2,rqLessOrEqual__r1_xreal_0__rm3_r3,rqLessOrEqual__r1_xreal_0__rm3_r4,rqLessOrEqual__r1_xreal_0__rm3_rm1,rqLessOrEqual__r1_xreal_0__rm3_rm3,rqLessOrEqual__r1_xreal_0__rm3_rn1d2,rqLessOrEqual__r1_xreal_0__rm3_rn1d4,rqLessOrEqual__r1_xreal_0__rm3_rnm3d4,rqLessOrEqual__r1_xreal_0__rm4_r2,rqLessOrEqual__r1_xreal_0__rm4_r4,rqLessOrEqual__r1_xreal_0__rm4_rm2,rqLessOrEqual__r1_xreal_0__rm4_rm4,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r3,rqLessOrEqual__r1_xreal_0__rn1d2_r4,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rm3,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d4,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d4,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn1d3_r0,rqLessOrEqual__r1_xreal_0__rn1d3_r1,rqLessOrEqual__r1_xreal_0__rn1d3_r2,rqLessOrEqual__r1_xreal_0__rn1d3_r3,rqLessOrEqual__r1_xreal_0__rn1d3_rm1,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn1d4_r0,rqLessOrEqual__r1_xreal_0__rn1d4_r1,rqLessOrEqual__r1_xreal_0__rn1d4_r2,rqLessOrEqual__r1_xreal_0__rn1d4_r3,rqLessOrEqual__r1_xreal_0__rn1d4_r4,rqLessOrEqual__r1_xreal_0__rn1d4_rm3,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d4,rqLessOrEqual__r1_xreal_0__rn1d4_rn3d4,rqLessOrEqual__r1_xreal_0__rn1d4_rnm1d4,rqLessOrEqual__r1_xreal_0__rn1d4_rnm3d4,rqLessOrEqual__r1_xreal_0__rn2d3_r0,rqLessOrEqual__r1_xreal_0__rn2d3_r1,rqLessOrEqual__r1_xreal_0__rn2d3_r2,rqLessOrEqual__r1_xreal_0__rn2d3_r3,rqLessOrEqual__r1_xreal_0__rn2d3_r4,rqLessOrEqual__r1_xreal_0__rn2d3_rm1,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn3d2_r0,rqLessOrEqual__r1_xreal_0__rn3d2_r1,rqLessOrEqual__r1_xreal_0__rn3d2_r2,rqLessOrEqual__r1_xreal_0__rn3d2_r3,rqLessOrEqual__r1_xreal_0__rn3d2_r4,rqLessOrEqual__r1_xreal_0__rn3d2_rm1,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d4,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn3d4_r0,rqLessOrEqual__r1_xreal_0__rn3d4_r1,rqLessOrEqual__r1_xreal_0__rn3d4_r2,rqLessOrEqual__r1_xreal_0__rn3d4_r3,rqLessOrEqual__r1_xreal_0__rn3d4_r4,rqLessOrEqual__r1_xreal_0__rn3d4_rm1,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d4,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d4,rqLessOrEqual__r1_xreal_0__rn3d4_rnm1d4,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_r4,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d4,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d4,rqLessOrEqual__r1_xreal_0__rnm1d3_r0,rqLessOrEqual__r1_xreal_0__rnm1d3_r1,rqLessOrEqual__r1_xreal_0__rnm1d3_r2,rqLessOrEqual__r1_xreal_0__rnm1d3_r3,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rnm1d4_r0,rqLessOrEqual__r1_xreal_0__rnm1d4_r1,rqLessOrEqual__r1_xreal_0__rnm1d4_r2,rqLessOrEqual__r1_xreal_0__rnm1d4_r3,rqLessOrEqual__r1_xreal_0__rnm1d4_r4,rqLessOrEqual__r1_xreal_0__rnm1d4_rm1,rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d4_rn1d4,rqLessOrEqual__r1_xreal_0__rnm1d4_rn3d4,rqLessOrEqual__r1_xreal_0__rnm1d4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rqRealMult__k3_xcmplx_0__rn4d3_r1_rn4d3,rqRealMult__k3_xcmplx_0__rn4d3_r3_r4,rqRealMult__k3_xcmplx_0__rn4d3_rn1d4_rn1d3,rqRealMult__k3_xcmplx_0__rn4d3_rn3d4_r1,rqRealMult__k3_xcmplx_0__rn4d3_rnm1d4_rnm1d3,rqRealMult__k3_xcmplx_0__rn4d3_rnm3d4_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_r4_rm2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm4_r2,rqRealMult__k3_xcmplx_0__rnm1d2_rn1d2_rnm1d4,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d2_rnm1d2_rn1d4,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm1d4_r1_rnm1d4,rqRealMult__k3_xcmplx_0__rnm1d4_r2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d4_r3_rnm3d4,rqRealMult__k3_xcmplx_0__rnm1d4_r4_rm1,rqRealMult__k3_xcmplx_0__rnm1d4_rm2_rn1d2,rqRealMult__k3_xcmplx_0__rnm1d4_rm3_rn3d4,rqRealMult__k3_xcmplx_0__rnm1d4_rm4_r1,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r2_rnm4d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm2_rn4d3,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn1d2_rnm3d4,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rn4d3_rm2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d2_rn3d4,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm4d3_r2,rqRealMult__k3_xcmplx_0__rnm3d4_r1_rnm3d4,rqRealMult__k3_xcmplx_0__rnm3d4_r2_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d4_r4_rm3,rqRealMult__k3_xcmplx_0__rnm3d4_rm2_rn3d2,rqRealMult__k3_xcmplx_0__rnm3d4_rm4_r3,rqRealMult__k3_xcmplx_0__rnm3d4_rn1d3_rnm1d4,rqRealMult__k3_xcmplx_0__rnm3d4_rn4d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d4_rnm4d3_r1,rqRealMult__k3_xcmplx_0__rnm4d3_r1_rnm4d3,rqRealMult__k3_xcmplx_0__rnm4d3_r3_rm4,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d4_rnm1d3,rqRealMult__k3_xcmplx_0__rnm4d3_rn3d4_rm1,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d2_rn2d3,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d4_rn1d3,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d2_r2,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d4_r1,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rm4_r4,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn1d4_rnm1d4,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rn3d4_rnm3d4,rqRealNeg__k4_xcmplx_0__rn4d3_rnm4d3,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm1d4_rn1d4,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,rqRealNeg__k4_xcmplx_0__rnm3d4_rn3d4,rqRealNeg__k4_xcmplx_0__rnm4d3_rn4d3,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc4_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,spc4_boole,e5_2_1_2_1__ali2,t3_seq_2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__r4_rm4,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_r4_rm4,rqRealDiff__k6_xcmplx_0__r2_r4_rm2,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r4_r0,rqLessOrEqual__r1_xreal_0__r4_r2]),
    [interesting(0.35),file(ali2,e6_2_1_2_1__ali2),[file(ali2,e6_2_1_2_1__ali2)]]).

fof(dt_c3_2_1_2_1__ali2,assumption,(
    $true ),
    introduced(assumption,[file(ali2,c3_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c3_2_1_2_1__ali2)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c3_2_1_2_1__ali2,definition,
    ( ~ ( r2_hidden(c3_2_1_2_1__ali2,k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2))
        & ~ r2_hidden(c3_2_1_2_1__ali2,c3_2_1_2__ali2) )
   => ! [A] : 
        ~ ( r2_hidden(A,k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2))
          & ~ r2_hidden(A,c3_2_1_2__ali2) ) ),
    introduced(definition,[new_symbol(c3_2_1_2_1__ali2),file(ali2,c3_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c3_2_1_2_1__ali2)]).

fof(e7_2_1_2_1__ali2,assumption,(
    r2_hidden(c3_2_1_2_1__ali2,k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2)) ),
    introduced(assumption,[file(ali2,e7_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,e7_2_1_2_1__ali2)]).

fof(de_c4_2_1_2_1__ali2,definition,(
    c4_2_1_2_1__ali2 = c3_2_1_2_1__ali2 ),
    introduced(definition,[new_symbol(c4_2_1_2_1__ali2),file(ali2,c4_2_1_2_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c4_2_1_2_1__ali2)]).

fof(e8_2_1_2_1__ali2,plain,(
    m1_subset_1(c3_2_1_2_1__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[dt_k2_zfmisc_1,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,cc1_xreal_0,reflexivity_r1_tarski,existence_m1_ali2,existence_m1_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_metric_1,dt_k3_power,dt_k5_ordinal2,dt_m1_ali2,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,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,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k4_metric_1,commutativity_k4_real_1,existence_l1_metric_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k5_real_1,dt_k6_real_1,dt_k8_funct_2,dt_l1_metric_1,dt_l1_struct_0,dt_m2_subset_1,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc15_membered,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_struct_0,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_subset,t5_arithm,t5_subset,t6_arithm,t6_boole,t8_boole,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k9_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2_1_2_1__ali2,de_c2_2_1_2_1__ali2,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_r3_rm3,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm3_r3,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3,rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_r3_rm2,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rm2_r3,rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3,rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2,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__r2_r3_rm1,rqRealDiff__k6_xcmplx_0__r2_rm1_r3,rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2,rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2,rqRealDiff__k6_xcmplx_0__r3_r0_r3,rqRealDiff__k6_xcmplx_0__r3_r1_r2,rqRealDiff__k6_xcmplx_0__r3_r2_r1,rqRealDiff__k6_xcmplx_0__r3_r3_r0,rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2,rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3,rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1,rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2,rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3,rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3,rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0,rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3,rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1,rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3,rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3,rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3,rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0,rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1,rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2,rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2,rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0,rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2,rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0,rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2,rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_r3_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3,rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3,rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2,rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3,rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2,rqRealDiv__k7_xcmplx_0__r3_r3_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,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_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0,rqRealMult__k3_xcmplx_0__r0_rn3d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e7_2_1_2_1__ali2,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]),
    [interesting(0.35),file(ali2,e8_2_1_2_1__ali2),[file(ali2,e8_2_1_2_1__ali2)]]).

fof(dt_c4_2_1_2_1__ali2,plain,(
    m1_subset_1(c4_2_1_2_1__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_metric_1,existence_l1_struct_0,dt_l1_metric_1,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,e8_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,c4_2_1_2_1__ali2),[file(ali2,c4_2_1_2_1__ali2)]]).

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(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(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(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(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(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_real_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_1),
    [interesting(0.9),axiom,file(real_1,k3_real_1)]).

fof(redefinition_k3_real_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_real_1),
    [interesting(0.9),axiom,file(real_1,k3_real_1)]).

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_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    [interesting(0.9),axiom,file(real_1,k3_real_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(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_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_r3_r3,theorem,(
    k2_xcmplx_0(0,3) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r3_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r3_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r0_r4_r4,theorem,(
    k2_xcmplx_0(0,4) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_r4_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r4_r4)]).

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__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__r0_rm3_rm3,theorem,(
    k2_xcmplx_0(0,k4_xcmplx_0(3)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rn1d4_rn1d4,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d4_rn1d4)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(2,3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(3,2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,theorem,(
    k2_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]).

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_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_r2_r3,theorem,(
    k2_xcmplx_0(1,2) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r2_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r1_r3_r4,theorem,(
    k2_xcmplx_0(1,3) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_r3_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r3_r4)]).

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__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__r1_rm3_rm2,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(3)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rm4_rm3,theorem,(
    k2_xcmplx_0(1,k4_xcmplx_0(4)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm4_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm4_rm3)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rn1d3_rn4d3,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(1,3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rn1d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rn1d3_rn4d3)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d4_rn3d4,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d4_rn3d4)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm3d2_rnm1d2,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm3d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm3d2_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r1_rnm3d4_rn1d4,theorem,(
    k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm3d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm3d4_rn1d4)]).

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_r1_r3,theorem,(
    k2_xcmplx_0(2,1) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r1_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r2_r2_r4,theorem,(
    k2_xcmplx_0(2,2) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_r2_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r2_r4)]).

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__r2_rm3_rm1,theorem,(
    k2_xcmplx_0(2,k4_xcmplx_0(3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rm4_rm2,theorem,(
    k2_xcmplx_0(2,k4_xcmplx_0(4)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm4_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm4_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2,theorem,(
    k2_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2,theorem,(
    k2_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(3),2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__r3_r0_r3,theorem,(
    k2_xcmplx_0(3,0) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_r0_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r0_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r3_r1_r4,theorem,(
    k2_xcmplx_0(3,1) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_r1_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_r1_r4)]).

fof(rqRealAdd__k2_xcmplx_0__r3_rm1_r2,theorem,(
    k2_xcmplx_0(3,k4_xcmplx_0(1)) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm1_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm1_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r3_rm2_r1,theorem,(
    k2_xcmplx_0(3,k4_xcmplx_0(2)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r3_rm3_r0,theorem,(
    k2_xcmplx_0(3,k4_xcmplx_0(3)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm3_r0)]).

fof(rqRealAdd__k2_xcmplx_0__r3_rm4_rm1,theorem,(
    k2_xcmplx_0(3,k4_xcmplx_0(4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r3_rm4_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__r4_r0_r4,theorem,(
    k2_xcmplx_0(4,0) = 4 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_r0_r4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_r0_r4)]).

fof(rqRealAdd__k2_xcmplx_0__r4_rm1_r3,theorem,(
    k2_xcmplx_0(4,k4_xcmplx_0(1)) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm1_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm1_r3)]).

fof(rqRealAdd__k2_xcmplx_0__r4_rm2_r2,theorem,(
    k2_xcmplx_0(4,k4_xcmplx_0(2)) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm2_r2)]).

fof(rqRealAdd__k2_xcmplx_0__r4_rm3_r1,theorem,(
    k2_xcmplx_0(4,k4_xcmplx_0(3)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm3_r1)]).

fof(rqRealAdd__k2_xcmplx_0__r4_rm4_r0,theorem,(
    k2_xcmplx_0(4,k4_xcmplx_0(4)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r4_rm4_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_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_r3_r2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),3) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r3_r2)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_r4_r3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),4) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r4_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r4_r3)]).

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__rm1_rm2_rm3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(3)) = k4_xcmplx_0(4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(3,2)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2)]).

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(rqRealAdd__k2_xcmplx_0__rm2_r3_r1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),3) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r3_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_r4_r2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),4) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r4_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r4_r2)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = k4_xcmplx_0(4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_rn2d3_rnm4d3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(2,3)) = k7_xcmplx_0(k4_xcmplx_0(4),3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rn2d3_rnm4d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rn2d3_rnm4d3)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(3,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rm2_rn4d3_rnm2d3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(4,3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rn4d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_rn4d3_rnm2d3)]).

fof(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(3),1) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(3),2) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm3_r3_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(3),3) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r3_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rm3_r4_r1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(3),4) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_r4_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(3),k4_xcmplx_0(1)) = k4_xcmplx_0(4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4)]).

fof(rqRealAdd__k2_xcmplx_0__rm4_r1_rm3,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(4),1) = k4_xcmplx_0(3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r1_rm3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r1_rm3)]).

fof(rqRealAdd__k2_xcmplx_0__rm4_r2_rm2,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(4),2) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r2_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rm4_r3_rm1,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(4),3) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r3_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rm4_r4_r0,theorem,(
    k2_xcmplx_0(k4_xcmplx_0(4),4) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm4_r4_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d4_rn3d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,4)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d4_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d4_rn3d4)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d4_rn1d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d4_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d4_rn1d4)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d4_rnm1d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d4_rnm1d4)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d3_r1_rn4d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,3),1) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_r1_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_r1_rn4d3)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(1,3)) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(2,3)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k7_xcmplx_0(k4_xcmplx_0(1),3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d4_r0_rn1d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,4),0) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_r0_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_r0_rn1d4)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d4_rn1d2_rn3d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(1,2)) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rn1d2_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rn1d2_rn3d4)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d4_rn1d4_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(1,4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rn1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rn1d4_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d4_rn3d4_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(3,4)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rn3d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rn3d4_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d4_rnm1d4_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rnm1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rnm1d4_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn1d4_rnm3d4_rnm1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(1,4),k7_xcmplx_0(k4_xcmplx_0(3),4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rnm3d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d4_rnm3d4_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(2,3),0) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3)]).

fof(rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(1,3)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn2d3_rn2d3_rn4d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(2,3)) = k7_xcmplx_0(4,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rn2d3_rn4d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rn2d3_rn4d3)]).

fof(rqRealAdd__k2_xcmplx_0__rn2d3_rn4d3_r2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(4,3)) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rn4d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rn4d3_r2)]).

fof(rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3)]).

fof(rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(2,3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),0) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(1,2)) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(3,2)) = 3 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d4_rn1d4_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(1,4)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rn1d4_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rn1d4_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d4_rn3d4_rn3d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(3,4)) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rn3d4_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rn3d4_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d4_rnm1d4_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rnm1d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rnm1d4_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rn3d4_rnm3d4_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(3,4),k7_xcmplx_0(k4_xcmplx_0(3),4)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rnm3d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn3d4_rnm3d4_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rn4d3_rn2d3_r2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(2,3)) = 2 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn4d3_rn2d3_r2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn4d3_rn2d3_r2)]).

fof(rqRealAdd__k2_xcmplx_0__rn4d3_rnm1d3_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(4,3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rn4d3_rnm1d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn4d3_rnm1d3_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) = k7_xcmplx_0(3,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(3),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d4_rnm1d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,4)) = k7_xcmplx_0(k4_xcmplx_0(1),4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d4_rnm1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d4_rnm1d4)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(3,2)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(3),2)) = k4_xcmplx_0(2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),1) = k7_xcmplx_0(2,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(1,3)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(2,3)) = k7_xcmplx_0(1,3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d3_rn4d3_r1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(4,3)) = 1 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rn4d3_r1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rn4d3_r1)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k7_xcmplx_0(k4_xcmplx_0(2),3) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),3),k7_xcmplx_0(k4_xcmplx_0(2),3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d4_r1_rn3d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),1) = k7_xcmplx_0(3,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_r1_rn3d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_r1_rn3d4)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d4_rn1d4_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(1,4)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_rn1d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_rn1d4_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d4_rn3d4_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(3,4)) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_rn3d4_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_rn3d4_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm1d4_rnm1d4_rnm1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_rnm1d4_rnm1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d4_rnm1d4_rnm1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(2,3)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2),3),k7_xcmplx_0(k4_xcmplx_0(1),3)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1)]).

fof(rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),2) = k7_xcmplx_0(1,2) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2)]).

fof(rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),2),k7_xcmplx_0(3,2)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm3d4_r1_rn1d4,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),1) = k7_xcmplx_0(1,4) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d4_r1_rn1d4),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d4_r1_rn1d4)]).

fof(rqRealAdd__k2_xcmplx_0__rnm3d4_rn3d4_r0,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(3,4)) = 0 ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d4_rn3d4_r0),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d4_rn3d4_r0)]).

fof(rqRealAdd__k2_xcmplx_0__rnm3d4_rnm1d4_rm1,theorem,(
    k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3),4),k7_xcmplx_0(k4_xcmplx_0(1),4)) = k4_xcmplx_0(1) ),
    file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d4_rnm1d4_rm1),
    [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm3d4_rnm1d4_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(t5_metric_1,theorem,(
    ! [A] : 
      ( ( v6_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_xreal_0(0,k4_metric_1(A,B,C)) ) ) ) ),
    file(metric_1,t5_metric_1),
    [interesting(0.9),axiom,file(metric_1,t5_metric_1)]).

fof(e15_2_1_2_1__ali2,plain,(
    r1_xreal_0(0,k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,cc1_xreal_0,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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_struct_0,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,dt_k4_metric_1,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,t5_metric_1]),
    [interesting(0.35),file(ali2,e15_2_1_2_1__ali2),[file(ali2,e15_2_1_2_1__ali2)]]).

fof(e2_2__ali2,plain,
    ( ~ r1_xreal_0(c3_2__ali2,0)
    & ~ r1_xreal_0(1,c3_2__ali2) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[dh_c3_2__ali2,e1_2__ali2]),
    [interesting(0.8),file(ali2,e2_2__ali2),[file(ali2,e2_2__ali2)]]).

fof(t147_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(0,A)
                & r1_xreal_0(B,1) )
              | ( r1_xreal_0(A,0)
                & r1_xreal_0(1,B) ) )
           => r1_xreal_0(k3_xcmplx_0(A,B),A) ) ) ) ),
    file(real_2,t147_real_2),
    [interesting(0.9),axiom,file(real_2,t147_real_2)]).

fof(e16_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,cc1_xreal_0,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_struct_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c3_2_1_2_1__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c3_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e15_2_1_2_1__ali2,e2_2__ali2,t147_real_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.35),file(ali2,e16_2_1_2_1__ali2),[file(ali2,e16_2_1_2_1__ali2)]]).

fof(e3_2__ali2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
         => r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B)),k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,A,B))) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[dh_c3_2__ali2,e1_2__ali2]),
    [interesting(0.8),file(ali2,e3_2__ali2),[file(ali2,e3_2__ali2)]]).

fof(e14_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e3_2__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e14_2_1_2_1__ali2),[file(ali2,e14_2_1_2_1__ali2)]]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t2_xreal_1)]).

fof(e17_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e16_2_1_2_1__ali2,e14_2_1_2_1__ali2,t2_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e17_2_1_2_1__ali2),[file(ali2,e17_2_1_2_1__ali2)]]).

fof(t8_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t8_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t8_xreal_1)]).

fof(e18_2_1_2_1__ali2,plain,(
    r1_xreal_0(k3_real_1(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2)),k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2),k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc6_arithm,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k2_xcmplx_0,dt_k3_real_1,dt_k4_metric_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc3_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e17_2_1_2_1__ali2,t8_xreal_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2]),
    [interesting(0.35),file(ali2,e18_2_1_2_1__ali2),[file(ali2,e18_2_1_2_1__ali2)]]).

fof(t9_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ),
    file(xreal_1,t9_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t9_xreal_1)]).

fof(e21_2_1_2_1__ali2,plain,(
    r1_xreal_0(k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2),k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)))),k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_real_1(2,k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,c1_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc3_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r1,rqRealMult__k3_xcmplx_0__r2_r1_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e18_2_1_2_1__ali2,t9_xreal_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.35),file(ali2,e21_2_1_2_1__ali2),[file(ali2,e21_2_1_2_1__ali2)]]).

fof(t4_metric_1,theorem,(
    ! [A] : 
      ( l1_metric_1(A)
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))) ) ) )
      <=> v9_metric_1(A) ) ) ),
    file(metric_1,t4_metric_1),
    [interesting(0.9),axiom,file(metric_1,t4_metric_1)]).

fof(e12_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k3_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc6_membered,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_real,t1_subset,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc2_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,fc3_xreal_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k2_metric_1,dt_k3_real_1,dt_k4_metric_1,dt_k8_funct_2,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,t4_metric_1]),
    [interesting(0.35),file(ali2,e12_2_1_2_1__ali2),[file(ali2,e12_2_1_2_1__ali2)]]).

fof(e10_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k3_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2),k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc6_membered,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,spc6_arithm,t1_real,t1_subset,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc2_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,fc3_xreal_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k2_metric_1,dt_k3_real_1,dt_k4_metric_1,dt_k8_funct_2,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,t4_metric_1]),
    [interesting(0.35),file(ali2,e10_2_1_2_1__ali2),[file(ali2,e10_2_1_2_1__ali2)]]).

fof(e11_2_1_2_1__ali2,plain,(
    r1_xreal_0(k3_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2))),k3_real_1(k3_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2),k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2))),k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc6_membered,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc7_xreal_0,fc1_struct_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc6_arithm,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k2_xcmplx_0,dt_k3_real_1,dt_k4_metric_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc3_xreal_0,e10_2_1_2_1__ali2,t8_xreal_1]),
    [interesting(0.35),file(ali2,e11_2_1_2_1__ali2),[file(ali2,e11_2_1_2_1__ali2)]]).

fof(e13_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k3_real_1(k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc6_membered,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k2_xcmplx_0,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc7_xreal_0,fc1_struct_0,fc2_membered,fc3_xreal_0,rc1_xreal_0,rc3_struct_0,spc6_arithm,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k3_real_1,dt_k4_metric_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,e12_2_1_2_1__ali2,e11_2_1_2_1__ali2,t2_xreal_1]),
    [interesting(0.35),file(ali2,e13_2_1_2_1__ali2),[file(ali2,e13_2_1_2_1__ali2)]]).

fof(e22_2_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_real_1(2,k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc3_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,rqRealAdd__k2_xcmplx_0__r1_r1_r2,spc5_arithm,spc6_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r1,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e21_2_1_2_1__ali2,e13_2_1_2_1__ali2,t2_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.35),file(ali2,e22_2_1_2_1__ali2),[file(ali2,e22_2_1_2_1__ali2)]]).

fof(t12_metric_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( l1_metric_1(B)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( r2_hidden(D,k9_metric_1(B,C,A))
                  <=> ( ~ v3_struct_0(B)
                      & ~ r1_xreal_0(A,k2_metric_1(B,C,D)) ) ) ) ) ) ) ),
    file(metric_1,t12_metric_1),
    [interesting(0.9),axiom,file(metric_1,t12_metric_1)]).

fof(e9_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(c2_2_1_2_1__ali2,k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[dt_k2_zfmisc_1,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,cc1_xreal_0,reflexivity_r1_tarski,existence_m1_ali2,existence_m1_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k3_power,dt_k5_ordinal2,dt_m1_ali2,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,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,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,commutativity_k4_real_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k5_real_1,dt_k6_real_1,dt_k8_funct_2,dt_l1_struct_0,dt_m2_subset_1,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc15_membered,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc2_membered,fc30_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t4_subset,t5_arithm,t5_subset,t6_arithm,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_l1_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,dt_k2_metric_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k9_metric_1,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2_1_2_1__ali2,dt_c4_2_1_2_1__ali2,de_c2_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r3,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm3,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rn1d3,rqLessOrEqual__r1_xreal_0__r0_rn2d3,rqLessOrEqual__r1_xreal_0__r0_rn3d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r3,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm3,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rn1d3,rqLessOrEqual__r1_xreal_0__r1_rn2d3,rqLessOrEqual__r1_xreal_0__r1_rn3d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r3,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm3,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rn1d3,rqLessOrEqual__r1_xreal_0__r2_rn2d3,rqLessOrEqual__r1_xreal_0__r2_rn3d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d3,rqLessOrEqual__r1_xreal_0__r2_rnm3d2,rqLessOrEqual__r1_xreal_0__r3_r0,rqLessOrEqual__r1_xreal_0__r3_r1,rqLessOrEqual__r1_xreal_0__r3_r2,rqLessOrEqual__r1_xreal_0__r3_r3,rqLessOrEqual__r1_xreal_0__r3_rm1,rqLessOrEqual__r1_xreal_0__r3_rm2,rqLessOrEqual__r1_xreal_0__r3_rm3,rqLessOrEqual__r1_xreal_0__r3_rn1d2,rqLessOrEqual__r1_xreal_0__r3_rn1d3,rqLessOrEqual__r1_xreal_0__r3_rn2d3,rqLessOrEqual__r1_xreal_0__r3_rn3d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r3,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rm3,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rn1d3,rqLessOrEqual__r1_xreal_0__rm1_rn2d3,rqLessOrEqual__r1_xreal_0__rm1_rn3d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r3,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm3_r0,rqLessOrEqual__r1_xreal_0__rm3_r1,rqLessOrEqual__r1_xreal_0__rm3_r2,rqLessOrEqual__r1_xreal_0__rm3_r3,rqLessOrEqual__r1_xreal_0__rm3_rm1,rqLessOrEqual__r1_xreal_0__rm3_rm3,rqLessOrEqual__r1_xreal_0__rm3_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r3,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rm3,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn1d3_r0,rqLessOrEqual__r1_xreal_0__rn1d3_r1,rqLessOrEqual__r1_xreal_0__rn1d3_r2,rqLessOrEqual__r1_xreal_0__rn1d3_r3,rqLessOrEqual__r1_xreal_0__rn1d3_rm1,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn2d3_r0,rqLessOrEqual__r1_xreal_0__rn2d3_r1,rqLessOrEqual__r1_xreal_0__rn2d3_r2,rqLessOrEqual__r1_xreal_0__rn2d3_r3,rqLessOrEqual__r1_xreal_0__rn2d3_rm1,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn3d2_r0,rqLessOrEqual__r1_xreal_0__rn3d2_r1,rqLessOrEqual__r1_xreal_0__rn3d2_r2,rqLessOrEqual__r1_xreal_0__rn3d2_r3,rqLessOrEqual__r1_xreal_0__rn3d2_rm1,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d3_r0,rqLessOrEqual__r1_xreal_0__rnm1d3_r1,rqLessOrEqual__r1_xreal_0__rnm1d3_r2,rqLessOrEqual__r1_xreal_0__rnm1d3_r3,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3,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_r3_rm3,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm3_r3,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3,rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_r3_rm2,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rm2_r3,rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3,rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2,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__r2_r3_rm1,rqRealDiff__k6_xcmplx_0__r2_rm1_r3,rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2,rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2,rqRealDiff__k6_xcmplx_0__r3_r0_r3,rqRealDiff__k6_xcmplx_0__r3_r1_r2,rqRealDiff__k6_xcmplx_0__r3_r2_r1,rqRealDiff__k6_xcmplx_0__r3_r3_r0,rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2,rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3,rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1,rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2,rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3,rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3,rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0,rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3,rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1,rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3,rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3,rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3,rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0,rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1,rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2,rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2,rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0,rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2,rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0,rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2,rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_r3_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3,rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3,rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2,rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3,rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2,rqRealDiv__k7_xcmplx_0__r3_r3_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,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_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0,rqRealMult__k3_xcmplx_0__r0_rn3d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e7_2_1_2_1__ali2,t12_metric_1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.35),file(ali2,e9_2_1_2_1__ali2),[file(ali2,e9_2_1_2_1__ali2)]]).

fof(t70_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(B,A)) ) ) ) ) ),
    file(xreal_1,t70_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t70_xreal_1)]).

fof(e19_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(k4_real_1(2,c2_2_1_2_1__ali2),k4_real_1(2,k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[dt_k2_zfmisc_1,fc4_subset_1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,cc1_xreal_0,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_power,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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,fc1_struct_0,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_struct_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k4_power,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_metric_1,dt_k4_power,dt_k5_numbers,dt_k5_real_1,dt_k6_real_1,dt_k8_funct_2,dt_l1_metric_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c3_2_1_2_1__ali2,dt_c4_2__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc23_xreal_0,fc2_membered,fc30_xreal_0,rc1_xreal_0,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2_1_2_1__ali2,dt_c4_2_1_2_1__ali2,de_c2_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r3,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm3,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rn1d3,rqLessOrEqual__r1_xreal_0__r0_rn2d3,rqLessOrEqual__r1_xreal_0__r0_rn3d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r3,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm3,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rn1d3,rqLessOrEqual__r1_xreal_0__r1_rn2d3,rqLessOrEqual__r1_xreal_0__r1_rn3d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r2_r3,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm3,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rn1d3,rqLessOrEqual__r1_xreal_0__r2_rn2d3,rqLessOrEqual__r1_xreal_0__r2_rn3d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d3,rqLessOrEqual__r1_xreal_0__r2_rnm3d2,rqLessOrEqual__r1_xreal_0__r3_r0,rqLessOrEqual__r1_xreal_0__r3_r1,rqLessOrEqual__r1_xreal_0__r3_r2,rqLessOrEqual__r1_xreal_0__r3_r3,rqLessOrEqual__r1_xreal_0__r3_rm1,rqLessOrEqual__r1_xreal_0__r3_rm2,rqLessOrEqual__r1_xreal_0__r3_rm3,rqLessOrEqual__r1_xreal_0__r3_rn1d2,rqLessOrEqual__r1_xreal_0__r3_rn1d3,rqLessOrEqual__r1_xreal_0__r3_rn2d3,rqLessOrEqual__r1_xreal_0__r3_rn3d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r3,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rm3,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rn1d3,rqLessOrEqual__r1_xreal_0__rm1_rn2d3,rqLessOrEqual__r1_xreal_0__rm1_rn3d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r3,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm3_r0,rqLessOrEqual__r1_xreal_0__rm3_r1,rqLessOrEqual__r1_xreal_0__rm3_r2,rqLessOrEqual__r1_xreal_0__rm3_r3,rqLessOrEqual__r1_xreal_0__rm3_rm1,rqLessOrEqual__r1_xreal_0__rm3_rm3,rqLessOrEqual__r1_xreal_0__rm3_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r3,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rm3,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn1d3_r0,rqLessOrEqual__r1_xreal_0__rn1d3_r1,rqLessOrEqual__r1_xreal_0__rn1d3_r2,rqLessOrEqual__r1_xreal_0__rn1d3_r3,rqLessOrEqual__r1_xreal_0__rn1d3_rm1,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn2d3_r0,rqLessOrEqual__r1_xreal_0__rn2d3_r1,rqLessOrEqual__r1_xreal_0__rn2d3_r2,rqLessOrEqual__r1_xreal_0__rn2d3_r3,rqLessOrEqual__r1_xreal_0__rn2d3_rm1,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn3d2_r0,rqLessOrEqual__r1_xreal_0__rn3d2_r1,rqLessOrEqual__r1_xreal_0__rn3d2_r2,rqLessOrEqual__r1_xreal_0__rn3d2_r3,rqLessOrEqual__r1_xreal_0__rn3d2_rm1,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d3_r0,rqLessOrEqual__r1_xreal_0__rnm1d3_r1,rqLessOrEqual__r1_xreal_0__rnm1d3_r2,rqLessOrEqual__r1_xreal_0__rnm1d3_r3,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r3_rm3,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm3_r3,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3,rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_r3_rm2,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rm2_r3,rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3,rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r3_rm1,rqRealDiff__k6_xcmplx_0__r2_rm1_r3,rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2,rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2,rqRealDiff__k6_xcmplx_0__r3_r0_r3,rqRealDiff__k6_xcmplx_0__r3_r1_r2,rqRealDiff__k6_xcmplx_0__r3_r2_r1,rqRealDiff__k6_xcmplx_0__r3_r3_r0,rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2,rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3,rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rm2_rm3_r1,rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm3_r0_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__rm3_rm3_r0,rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2,rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2,rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3,rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3,rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0,rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3,rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1,rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3,rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3,rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3,rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0,rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1,rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2,rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2,rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1,rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0,rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2,rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3,rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0,rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0,rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2,rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r0_r3_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3,rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3,rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2,rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3,rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2,rqRealDiv__k7_xcmplx_0__r3_r3_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,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_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0,rqRealMult__k3_xcmplx_0__r0_rn3d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e9_2_1_2_1__ali2,t70_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r0]),
    [interesting(0.35),file(ali2,e19_2_1_2_1__ali2),[file(ali2,e19_2_1_2_1__ali2)]]).

fof(e20_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_real_1(2,c2_2_1_2_1__ali2)),k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_real_1(2,k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c4_2_1_2_1__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_power,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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_ordinal2,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k4_power,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k4_power,dt_k5_numbers,dt_k5_real_1,dt_k6_real_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c3_2_1_2_1__ali2,dt_c4_2__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2_1__ali2,dt_c4_2_1_2_1__ali2,de_c2_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc1_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r3,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm3,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rn1d3,rqLessOrEqual__r1_xreal_0__r0_rn2d3,rqLessOrEqual__r1_xreal_0__r0_rn3d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r3,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm3,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rn1d3,rqLessOrEqual__r1_xreal_0__r1_rn2d3,rqLessOrEqual__r1_xreal_0__r1_rn3d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r3,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm3,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rn1d3,rqLessOrEqual__r1_xreal_0__r2_rn2d3,rqLessOrEqual__r1_xreal_0__r2_rn3d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d3,rqLessOrEqual__r1_xreal_0__r2_rnm3d2,rqLessOrEqual__r1_xreal_0__r3_r0,rqLessOrEqual__r1_xreal_0__r3_r1,rqLessOrEqual__r1_xreal_0__r3_r2,rqLessOrEqual__r1_xreal_0__r3_r3,rqLessOrEqual__r1_xreal_0__r3_rm1,rqLessOrEqual__r1_xreal_0__r3_rm2,rqLessOrEqual__r1_xreal_0__r3_rm3,rqLessOrEqual__r1_xreal_0__r3_rn1d2,rqLessOrEqual__r1_xreal_0__r3_rn1d3,rqLessOrEqual__r1_xreal_0__r3_rn2d3,rqLessOrEqual__r1_xreal_0__r3_rn3d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r3,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rm3,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rn1d3,rqLessOrEqual__r1_xreal_0__rm1_rn2d3,rqLessOrEqual__r1_xreal_0__rm1_rn3d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r3,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm3_r0,rqLessOrEqual__r1_xreal_0__rm3_r1,rqLessOrEqual__r1_xreal_0__rm3_r2,rqLessOrEqual__r1_xreal_0__rm3_r3,rqLessOrEqual__r1_xreal_0__rm3_rm1,rqLessOrEqual__r1_xreal_0__rm3_rm3,rqLessOrEqual__r1_xreal_0__rm3_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r3,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rm3,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn1d3_r0,rqLessOrEqual__r1_xreal_0__rn1d3_r1,rqLessOrEqual__r1_xreal_0__rn1d3_r2,rqLessOrEqual__r1_xreal_0__rn1d3_r3,rqLessOrEqual__r1_xreal_0__rn1d3_rm1,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn2d3_r0,rqLessOrEqual__r1_xreal_0__rn2d3_r1,rqLessOrEqual__r1_xreal_0__rn2d3_r2,rqLessOrEqual__r1_xreal_0__rn2d3_r3,rqLessOrEqual__r1_xreal_0__rn2d3_rm1,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn3d2_r0,rqLessOrEqual__r1_xreal_0__rn3d2_r1,rqLessOrEqual__r1_xreal_0__rn3d2_r2,rqLessOrEqual__r1_xreal_0__rn3d2_r3,rqLessOrEqual__r1_xreal_0__rn3d2_rm1,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d3_r0,rqLessOrEqual__r1_xreal_0__rnm1d3_r1,rqLessOrEqual__r1_xreal_0__rnm1d3_r2,rqLessOrEqual__r1_xreal_0__rnm1d3_r3,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rnm1d3,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_r3_r3,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3,rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2,rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3,rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3,rqRealAdd__k2_xcmplx_0__r1_rnm3d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1,rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2,rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2,rqRealAdd__k2_xcmplx_0__r3_r0_r3,rqRealAdd__k2_xcmplx_0__r3_rm1_r2,rqRealAdd__k2_xcmplx_0__r3_rm2_r1,rqRealAdd__k2_xcmplx_0__r3_rm3_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_r3_r2,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3,rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2,rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rm2_r3_r1,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,rqRealAdd__k2_xcmplx_0__rm3_r3_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1,rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3,rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1,rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0,rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3,rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3,rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1,rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3,rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0,rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2,rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2,rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2,rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2,rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3,rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1,rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,r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qRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2,rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3,rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2,rqRealDiv__k7_xcmplx_0__r3_r3_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,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_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0,rqRealMult__k3_xcmplx_0__r0_rn3d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e19_2_1_2_1__ali2,t8_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.35),file(ali2,e20_2_1_2_1__ali2),[file(ali2,e20_2_1_2_1__ali2)]]).

fof(e23_2_1_2_1__ali2,plain,(
    ~ r1_xreal_0(k3_real_1(k4_metric_1(c1_2__ali2,c4_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2_1_2_1__ali2)),k4_real_1(2,c2_2_1_2_1__ali2)),k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_power,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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_ordinal2,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k4_power,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k4_power,dt_k5_numbers,dt_k5_real_1,dt_k6_real_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c3_2_1_2_1__ali2,dt_c4_2__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc3_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,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_r3_r3,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3,rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2,rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3,rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3,rqRealAdd__k2_xcmplx_0__r1_rnm3d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1,rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2,rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2,rqRealAdd__k2_xcmplx_0__r3_r0_r3,rqRealAdd__k2_xcmplx_0__r3_rm1_r2,rqRealAdd__k2_xcmplx_0__r3_rm2_r1,rqRealAdd__k2_xcmplx_0__r3_rm3_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_r3_r2,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3,rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2,rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rm2_r3_r1,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,rqRealAdd__k2_xcmplx_0__rm3_r3_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1,rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3,rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1,rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0,rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3,rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3,rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1,rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3,rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0,rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2,rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2,rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2,rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2,rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3,rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1,rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2,rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3,rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0,rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1,rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0,rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1,rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2,rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2_1__ali2,dt_c4_2_1_2_1__ali2,de_c2_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r3,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm3,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rn1d3,rqLessOrEqual__r1_xreal_0__r0_rn2d3,rqLessOrEqual__r1_xreal_0__r0_rn3d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r3,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm3,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rn1d3,rqLessOrEqual__r1_xreal_0__r1_rn2d3,rqLessOrEqual__r1_xreal_0__r1_rn3d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r3,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm3,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rn1d3,rqLessOrEqual__r1_xreal_0__r2_rn2d3,rqLessOrEqual__r1_xreal_0__r2_rn3d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d3,rqLessOrEqual__r1_xreal_0__r2_rnm3d2,rqLessOrEqual__r1_xreal_0__r3_r0,rqLessOrEqual__r1_xreal_0__r3_r1,rqLessOrEqual__r1_xreal_0__r3_r2,rqLessOrEqual__r1_xreal_0__r3_r3,rqLessOrEqual__r1_xreal_0__r3_rm1,rqLessOrEqual__r1_xreal_0__r3_rm2,rqLessOrEqual__r1_xreal_0__r3_rm3,rqLessOrEqual__r1_xreal_0__r3_rn1d2,rqLessOrEqual__r1_xreal_0__r3_rn1d3,rqLessOrEqual__r1_xreal_0__r3_rn2d3,rqLessOrEqual__r1_xreal_0__r3_rn3d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r3,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rm3,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rn1d3,rqLessOrEqual__r1_xreal_0__rm1_rn2d3,rqLessOrEqual__r1_xreal_0__rm1_rn3d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r3,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm3_r0,rqLessOrEqual__r1_xreal_0__rm3_r1,rqLessOrEqual__r1_xreal_0__rm3_r2,rqLessOrEqual__r1_xreal_0__rm3_r3,rqLessOrEqual__r1_xreal_0__rm3_rm1,rqLessOrEqual__r1_xreal_0__rm3_rm3,rqLessOrEqual__r1_xreal_0__rm3_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r3,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rm3,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn1d3_r0,rqLessOrEqual__r1_xreal_0__rn1d3_r1,rqLessOrEqual__r1_xreal_0__rn1d3_r2,rqLessOrEqual__r1_xreal_0__rn1d3_r3,rqLessOrEqual__r1_xreal_0__rn1d3_rm1,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn2d3_r0,rqLessOrEqual__r1_xreal_0__rn2d3_r1,rqLessOrEqual__r1_xreal_0__rn2d3_r2,rqLessOrEqual__r1_xreal_0__rn2d3_r3,rqLessOrEqual__r1_xreal_0__rn2d3_rm1,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn3d2_r0,rqLessOrEqual__r1_xreal_0__rn3d2_r1,rqLessOrEqual__r1_xreal_0__rn3d2_r2,rqLessOrEqual__r1_xreal_0__rn3d2_r3,rqLessOrEqual__r1_xreal_0__rn3d2_rm1,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2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k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,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_r3_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rm3_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d3_r0,rqRealMult__k3_xcmplx_0__r0_rn3d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r3_r3,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm3_rm3,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3,rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3,rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3,rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3,rqRealMult__k3_xcmplx_0__r2_rn3d2_r3,rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3,rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3,rqRealMult__k3_xcmplx_0__r3_r0_r0,rqRealMult__k3_xcmplx_0__r3_r1_r3,rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2,rqRealMult__k3_xcmplx_0__r3_rn1d3_r1,rqRealMult__k3_xcmplx_0__r3_rn2d3_r2,rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2,rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1,rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3,rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3,rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3,rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3,rqRealMult__k3_xcmplx_0__rm3_r0_r0,rqRealMult__k3_xcmplx_0__rm3_r1_rm3,rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2,rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1,rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2,rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1,rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,e22_2_1_2_1__ali2,e20_2_1_2_1__ali2,t2_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2,rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.35),file(ali2,e23_2_1_2_1__ali2),[file(ali2,e23_2_1_2_1__ali2)]]).

fof(e2_2_1_2_1__ali2,plain,(
    k5_real_1(k4_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c1_2_1_2_1__ali2)),k4_real_1(2,c2_2_1_2_1__ali2)) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_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,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc4_subset_1,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc30_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_membered,fc5_xreal_0,fc6_membered,fc6_xreal_0,fc8_xreal_0,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k6_real_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_k6_real_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_real_1,redefinition_k8_funct_2,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_real_1,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,de_c2_2_1_2_1__ali2,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_r3_r3,rqRealAdd__k2_xcmplx_0__r0_r4_r4,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rm3_rm3,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rn1d4_rn1d4,rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3,rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_r2_r3,rqRealAdd__k2_xcmplx_0__r1_r3_r4,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rm3_rm2,rqRealAdd__k2_xcmplx_0__r1_rm4_rm3,rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2,rqRealAdd__k2_xcmplx_0__r1_rn1d3_rn4d3,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3,rqRealAdd__k2_xcmplx_0__r1_rnm1d4_rn3d4,rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3,rqRealAdd__k2_xcmplx_0__r1_rnm3d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_rnm3d4_rn1d4,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_r1_r3,rqRealAdd__k2_xcmplx_0__r2_r2_r4,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__r2_rm3_rm1,rqRealAdd__k2_xcmplx_0__r2_rm4_rm2,rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2,rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2,rqRealAdd__k2_xcmplx_0__r3_r0_r3,rqRealAdd__k2_xcmplx_0__r3_r1_r4,rqRealAdd__k2_xcmplx_0__r3_rm1_r2,rqRealAdd__k2_xcmplx_0__r3_rm2_r1,rqRealAdd__k2_xcmplx_0__r3_rm3_r0,rqRealAdd__k2_xcmplx_0__r3_rm4_rm1,rqRealAdd__k2_xcmplx_0__r4_r0_r4,rqRealAdd__k2_xcmplx_0__r4_rm1_r3,rqRealAdd__k2_xcmplx_0__r4_rm2_r2,rqRealAdd__k2_xcmplx_0__r4_rm3_r1,rqRealAdd__k2_xcmplx_0__r4_rm4_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_r3_r2,rqRealAdd__k2_xcmplx_0__rm1_r4_r3,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3,rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3,rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2,rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rm2_r3_r1,rqRealAdd__k2_xcmplx_0__rm2_r4_r2,rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3,rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4,rqRealAdd__k2_xcmplx_0__rm2_rn2d3_rnm4d3,rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm2_rn4d3_rnm2d3,rqRealAdd__k2_xcmplx_0__rm3_r1_rm2,rqRealAdd__k2_xcmplx_0__rm3_r2_rm1,rqRealAdd__k2_xcmplx_0__rm3_r3_r0,rqRealAdd__k2_xcmplx_0__rm3_r4_r1,rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4,rqRealAdd__k2_xcmplx_0__rm4_r1_rm3,rqRealAdd__k2_xcmplx_0__rm4_r2_rm2,rqRealAdd__k2_xcmplx_0__rm4_r3_rm1,rqRealAdd__k2_xcmplx_0__rm4_r4_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d4_rn3d4,rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d4_rn1d4,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1,rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d4_rnm1d4,rqRealAdd__k2_xcmplx_0__rn1d3_r1_rn4d3,rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3,rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1,rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0,rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3,rqRealAdd__k2_xcmplx_0__rn1d4_r0_rn1d4,rqRealAdd__k2_xcmplx_0__rn1d4_rn1d2_rn3d4,rqRealAdd__k2_xcmplx_0__rn1d4_rn1d4_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d4_rn3d4_r1,rqRealAdd__k2_xcmplx_0__rn1d4_rnm1d4_r0,rqRealAdd__k2_xcmplx_0__rn1d4_rnm3d4_rnm1d2,rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3,rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1,rqRealAdd__k2_xcmplx_0__rn2d3_rn2d3_rn4d3,rqRealAdd__k2_xcmplx_0__rn2d3_rn4d3_r2,rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3,rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0,rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2,rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2,rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2,rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2,rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3,rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1,rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0,rqRealAdd__k2_xcmplx_0__rn3d4_rn1d4_r1,rqRealAdd__k2_xcmplx_0__rn3d4_rn3d4_rn3d2,rqRealAdd__k2_xcmplx_0__rn3d4_rnm1d4_rn1d2,rqRealAdd__k2_xcmplx_0__rn3d4_rnm3d4_r0,rqRealAdd__k2_xcmplx_0__rn4d3_rn2d3_r2,rqRealAdd__k2_xcmplx_0__rn4d3_rnm1d3_r1,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d4_rnm1d4,rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2,rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3,rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0,rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3,rqRealAdd__k2_xcmplx_0__rnm1d3_rn4d3_r1,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3,rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1,rqRealAdd__k2_xcmplx_0__rnm1d4_r1_rn3d4,rqRealAdd__k2_xcmplx_0__rnm1d4_rn1d4_r0,rqRealAdd__k2_xcmplx_0__rnm1d4_rn3d4_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d4_rnm1d4_rnm1d2,rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0,rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1,rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2,rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0,rqRealAdd__k2_xcmplx_0__rnm3d4_r1_rn1d4,rqRealAdd__k2_xcmplx_0__rnm3d4_rn3d4_r0,rqRealAdd__k2_xcmplx_0__rnm3d4_rnm1d4_rm1,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_r3_rm3,rqRealDiff__k6_xcmplx_0__r0_r4_rm4,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm3_r3,rqRealDiff__k6_xcmplx_0__r0_rm4_r4,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3,rqRealDiff__k6_xcmplx_0__r0_rn1d4_rnm1d4,rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3,rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2,rqRealDiff__k6_xcmplx_0__r0_rn3d4_rnm3d4,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d4_rn1d4,rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r3_rm2,rqRealDiff__k6_xcmplx_0__r1_r4_rm3,rqRealDiff__k6_xcmplx_0__r1_rm2_r3,rqRealDiff__k6_xcmplx_0__r1_rm3_r4,rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3,rqRealDiff__k6_xcmplx_0__r1_rn1d4_rn3d4,rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3,rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r1_rn3d4_rn1d4,rqRealDiff__k6_xcmplx_0__r1_rn4d3_rnm1d3,rqRealDiff__k6_xcmplx_0__r1_rnm1d3_rn4d3,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r3_rm1,rqRealDiff__k6_xcmplx_0__r2_r4_rm2,rqRealDiff__k6_xcmplx_0__r2_rm1_r3,rqRealDiff__k6_xcmplx_0__r2_rm2_r4,rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2,rqRealDiff__k6_xcmplx_0__r2_rn2d3_rn4d3,rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_rn4d3_rn2d3,rqRealDiff__k6_xcmplx_0__r3_r0_r3,rqRealDiff__k6_xcmplx_0__r3_r1_r2,rqRealDiff__k6_xcmplx_0__r3_r2_r1,rqRealDiff__k6_xcmplx_0__r3_r3_r0,rqRealDiff__k6_xcmplx_0__r3_r4_rm1,rqRealDiff__k6_xcmplx_0__r3_rm1_r4,rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2,rqRealDiff__k6_xcmplx_0__r4_r0_r4,rqRealDiff__k6_xcmplx_0__r4_r1_r3,rqRealDiff__k6_xcmplx_0__r4_r2_r2,rqRealDiff__k6_xcmplx_0__r4_r3_r1,rqRealDiff__k6_xcmplx_0__r4_r4_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_r2_rm3,rqRealDiff__k6_xcmplx_0__rm1_r3_rm4,rqRealDiff__k6_xcmplx_0__rm1_rm3_r2,rqRealDiff__k6_xcmplx_0__rm1_rm4_r3,rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2,rq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rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2,rqRealMult__k3_xcmplx_0__rn1d2_r4_r2,rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2,rqRealMult__k3_xcmplx_0__rn1d2_rm4_rm2,rqRealMult__k3_xcmplx_0__rn1d2_rn1d2_rn1d4,rqRealMult__k3_xcmplx_0__rn1d2_rn3d2_rn3d4,rqRealMult__k3_xcmplx_0__rn1d2_rnm1d2_rnm1d4,rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3,rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3,rqRealMult__k3_xcmplx_0__rn1d3_r3_r1,rqRealMult__k3_xcmplx_0__rn1d3_r4_rn4d3,rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3,rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1,rqRealMult__k3_xcmplx_0__rn1d4_r0_r0,rqRealMult__k3_xcmplx_0__rn1d4_r1_rn1d4,rqRealMult__k3_xcmplx_0__rn1d4_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d4_r3_rn3d4,rqRealMult__k3_xcmplx_0__rn1d4_r4_r1,rqRealMult__k3_xcmplx_0__rn1d4_rm2_rnm1d2,rqRealMult__k3_xcmplx_0__rn1d4_rm3_rnm3d4,rqRealMult__k3_xcmplx_0__rn1d4_rm4_rm1,rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3,rqRealMult__k3_xcmplx_0__rn2d3_r2_rn4d3,rqRealMult__k3_xcmplx_0__rn2d3_r3_r2,rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2,rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3,rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1,rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1,rqRealMult__k3_xcmplx_0__rn3d2_r0_r0,rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2,rqRealMult__k3_xcmplx_0__rn3d2_r2_r3,rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3,rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2,rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1,rqRealMult__k3_xcmplx_0__rn3d2_rn4d3_r2,rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2,rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1,rqRealMult__k3_xcmplx_0__rn3d2_rnm4d3_rm2,rqRealMult__k3_xcmplx_0__rn3d4_r1_rn3d4,rqRealMult__k3_xcmplx_0__rn3d4_r2_rn3d2,rqRealMult__k3_xcmplx_0__rn3d4_r4_r3,rqRealMult__k3_xcmplx_0__rn3d4_rm2_rnm3d2,rqRealMult__k3_xcmplx_0__rn3d4_rm4_rm3,rqRealMult__k3_xcmplx_0__rn3d4_rn4d3_r1,rqRealMult__k3_xcmplx_0__rn3d4_rnm4d3_rm1,rqRealMult__k3_xcmplx_0__rn4d3_r1_rn4d3,rqRealMult__k3_xcmplx_0__rn4d3_r3_r4,rqRealMult__k3_xcmplx_0__rn4d3_rn1d4_rn1d3,rqRealMult__k3_xcmplx_0__rn4d3_rn3d4_r1,rqRealMult__k3_xcmplx_0__rn4d3_rnm1d4_rnm1d3,rqRealMult__k3_xcmplx_0__rn4d3_rnm3d4_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_r4_rm2,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm4_r2,rqRealMult__k3_xcmplx_0__rnm1d2_rn1d2_rnm1d4,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d2_rnm1d2_rn1d4,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm1d4_r1_rnm1d4,rqRealMult__k3_xcmplx_0__rnm1d4_r2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d4_r3_rnm3d4,rqRealMult__k3_xcmplx_0__rnm1d4_r4_rm1,rqRealMult__k3_xcmplx_0__rnm1d4_rm2_rn1d2,rqRealMult__k3_xcmplx_0__rnm1d4_rm3_rn3d4,rqRealMult__k3_xcmplx_0__rnm1d4_rm4_r1,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r2_rnm4d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm2_rn4d3,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn1d2_rnm3d4,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rn4d3_rm2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d2_rn3d4,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm4d3_r2,rqRealMult__k3_xcmplx_0__rnm3d4_r1_rnm3d4,rqRealMult__k3_xcmplx_0__rnm3d4_r2_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d4_r4_rm3,rqRealMult__k3_xcmplx_0__rnm3d4_rm2_rn3d2,rqRealMult__k3_xcmplx_0__rnm3d4_rm4_r3,rqRealMult__k3_xcmplx_0__rnm3d4_rn1d3_rnm1d4,rqRealMult__k3_xcmplx_0__rnm3d4_rn4d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d4_rnm4d3_r1,rqRealMult__k3_xcmplx_0__rnm4d3_r1_rnm4d3,rqRealMult__k3_xcmplx_0__rnm4d3_r3_rm4,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d4_rnm1d3,rqRealMult__k3_xcmplx_0__rnm4d3_rn3d4_rm1,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d2_rn2d3,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d4_rn1d3,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d2_r2,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d4_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__r4_rm4,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rm4_r4,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn1d4_rnm1d4,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rn3d4_rnm3d4,rqRealNeg__k4_xcmplx_0__rn4d3_rnm4d3,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm1d4_rn1d4,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,rqRealNeg__k4_xcmplx_0__rnm3d4_rn3d4,rqRealNeg__k4_xcmplx_0__rnm4d3_rn4d3,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc4_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,spc4_boole,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rm2_r2_rm4,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1]),
    [interesting(0.35),file(ali2,e2_2_1_2_1__ali2),[file(ali2,e2_2_1_2_1__ali2)]]).

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(e24_2_1_2_1__ali2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
     => ~ ( c4_2_1_2_1__ali2 = A
          & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_2__ali2))) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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_ordinal2,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_k6_real_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_k6_real_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc30_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc1_arithm,spc2_arithm,spc4_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_arithm,t4_real,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_real_1,redefinition_k8_funct_2,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_real_1,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,dt_c4_2_1_2_1__ali2,de_c2_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,cc2_xreal_0,fc1_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_xreal_0,fc6_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r3,rqLessOrEqual__r1_xreal_0__r0_r4,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm3,rqLessOrEqual__r1_xreal_0__r0_rm4,rqLessOrEqual__r1_xreal_0__r0_rn1d2,rqLessOrEqual__r1_xreal_0__r0_rn1d3,rqLessOrEqual__r1_xreal_0__r0_rn1d4,rqLessOrEqual__r1_xreal_0__r0_rn2d3,rqLessOrEqual__r1_xreal_0__r0_rn3d2,rqLessOrEqual__r1_xreal_0__r0_rn3d4,rqLessOrEqual__r1_xreal_0__r0_rn4d3,rqLessOrEqual__r1_xreal_0__r0_rnm1d2,rqLessOrEqual__r1_xreal_0__r0_rnm1d3,rqLessOrEqual__r1_xreal_0__r0_rnm1d4,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r3,rqLessOrEqual__r1_xreal_0__r1_r4,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm3,rqLessOrEqual__r1_xreal_0__r1_rm4,rqLessOrEqual__r1_xreal_0__r1_rn1d2,rqLessOrEqual__r1_xreal_0__r1_rn1d3,rqLessOrEqual__r1_xreal_0__r1_rn1d4,rqLessOrEqual__r1_xreal_0__r1_rn2d3,rqLessOrEqual__r1_xreal_0__r1_rn3d2,rqLessOrEqual__r1_xreal_0__r1_rn3d4,rqLessOrEqual__r1_xreal_0__r1_rn4d3,rqLessOrEqual__r1_xreal_0__r1_rnm1d2,rqLessOrEqual__r1_xreal_0__r1_rnm1d3,rqLessOrEqual__r1_xreal_0__r1_rnm1d4,rqLessOrEqual__r1_xreal_0__r1_rnm3d2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r3,rqLessOrEqual__r1_xreal_0__r2_r4,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm3,rqLessOrEqual__r1_xreal_0__r2_rm4,rqLessOrEqual__r1_xreal_0__r2_rn1d2,rqLessOrEqual__r1_xreal_0__r2_rn1d3,rqLessOrEqual__r1_xreal_0__r2_rn1d4,rqLessOrEqual__r1_xreal_0__r2_rn2d3,rqLessOrEqual__r1_xreal_0__r2_rn3d2,rqLessOrEqual__r1_xreal_0__r2_rn3d4,rqLessOrEqual__r1_xreal_0__r2_rnm1d2,rqLessOrEqual__r1_xreal_0__r2_rnm1d3,rqLessOrEqual__r1_xreal_0__r2_rnm3d2,rqLessOrEqual__r1_xreal_0__r3_r0,rqLessOrEqual__r1_xreal_0__r3_r1,rqLessOrEqual__r1_xreal_0__r3_r2,rqLessOrEqual__r1_xreal_0__r3_r3,rqLessOrEqual__r1_xreal_0__r3_r4,rqLessOrEqual__r1_xreal_0__r3_rm1,rqLessOrEqual__r1_xreal_0__r3_rm2,rqLessOrEqual__r1_xreal_0__r3_rm3,rqLessOrEqual__r1_xreal_0__r3_rm4,rqLessOrEqual__r1_xreal_0__r3_rn1d2,rqLessOrEqual__r1_xreal_0__r3_rn1d3,rqLessOrEqual__r1_xreal_0__r3_rn1d4,rqLessOrEqual__r1_xreal_0__r3_rn2d3,rqLessOrEqual__r1_xreal_0__r3_rn3d2,rqLessOrEqual__r1_xreal_0__r3_rn3d4,rqLessOrEqual__r1_xreal_0__r3_rnm1d2,rqLessOrEqual__r1_xreal_0__r3_rnm1d3,rqLessOrEqual__r1_xreal_0__r4_r0,rqLessOrEqual__r1_xreal_0__r4_r1,rqLessOrEqual__r1_xreal_0__r4_r2,rqLessOrEqual__r1_xreal_0__r4_r3,rqLessOrEqual__r1_xreal_0__r4_r4,rqLessOrEqual__r1_xreal_0__r4_rm1,rqLessOrEqual__r1_xreal_0__r4_rm2,rqLessOrEqual__r1_xreal_0__r4_rm3,rqLessOrEqual__r1_xreal_0__r4_rm4,rqLessOrEqual__r1_xreal_0__r4_rn1d2,rqLessOrEqual__r1_xreal_0__r4_rn1d4,rqLessOrEqual__r1_xreal_0__r4_rn2d3,rqLessOrEqual__r1_xreal_0__r4_rn3d2,rqLessOrEqual__r1_xreal_0__r4_rn3d4,rqLessOrEqual__r1_xreal_0__r4_rnm1d4,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r3,rqLessOrEqual__r1_xreal_0__rm1_r4,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm1_rm3,rqLessOrEqual__r1_xreal_0__rm1_rn1d2,rqLessOrEqual__r1_xreal_0__rm1_rn1d3,rqLessOrEqual__r1_xreal_0__rm1_rn1d4,rqLessOrEqual__r1_xreal_0__rm1_rn2d3,rqLessOrEqual__r1_xreal_0__rm1_rn3d2,rqLessOrEqual__r1_xreal_0__rm1_rn3d4,rqLessOrEqual__r1_xreal_0__rm1_rnm1d2,rqLessOrEqual__r1_xreal_0__rm1_rnm1d3,rqLessOrEqual__r1_xreal_0__rm1_rnm1d4,rqLessOrEqual__r1_xreal_0__rm1_rnm3d2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r3,rqLessOrEqual__r1_xreal_0__rm2_r4,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm2_rn1d4,rqLessOrEqual__r1_xreal_0__rm3_r0,rqLessOrEqual__r1_xreal_0__rm3_r1,rqLessOrEqual__r1_xreal_0__rm3_r2,rqLessOrEqual__r1_xreal_0__rm3_r3,rqLessOrEqual__r1_xreal_0__rm3_r4,rqLessOrEqual__r1_xreal_0__rm3_rm1,rqLessOrEqual__r1_xreal_0__rm3_rm3,rqLessOrEqual__r1_xreal_0__rm3_rn1d2,rqLessOrEqual__r1_xreal_0__rm3_rn1d4,rqLessOrEqual__r1_xreal_0__rm3_rnm3d4,rqLessOrEqual__r1_xreal_0__rm4_r2,rqLessOrEqual__r1_xreal_0__rm4_r4,rqLessOrEqual__r1_xreal_0__rm4_rm2,rqLessOrEqual__r1_xreal_0__rm4_rm4,rqLessOrEqual__r1_xreal_0__rn1d2_r0,rqLessOrEqual__r1_xreal_0__rn1d2_r1,rqLessOrEqual__r1_xreal_0__rn1d2_r2,rqLessOrEqual__r1_xreal_0__rn1d2_r3,rqLessOrEqual__r1_xreal_0__rn1d2_r4,rqLessOrEqual__r1_xreal_0__rn1d2_rm1,rqLessOrEqual__r1_xreal_0__rn1d2_rm3,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn1d4,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn1d2_rn3d4,rqLessOrEqual__r1_xreal_0__rn1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn1d3_r0,rqLessOrEqual__r1_xreal_0__rn1d3_r1,rqLessOrEqual__r1_xreal_0__rn1d3_r2,rqLessOrEqual__r1_xreal_0__rn1d3_r3,rqLessOrEqual__r1_xreal_0__rn1d3_rm1,rqLessOrEqual__r1_xreal_0__rn1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn1d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn1d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn1d4_r0,rqLessOrEqual__r1_xreal_0__rn1d4_r1,rqLessOrEqual__r1_xreal_0__rn1d4_r2,rqLessOrEqual__r1_xreal_0__rn1d4_r3,rqLessOrEqual__r1_xreal_0__rn1d4_r4,rqLessOrEqual__r1_xreal_0__rn1d4_rm3,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d2,rqLessOrEqual__r1_xreal_0__rn1d4_rn1d4,rqLessOrEqual__r1_xreal_0__rn1d4_rn3d4,rqLessOrEqual__r1_xreal_0__rn1d4_rnm1d4,rqLessOrEqual__r1_xreal_0__rn1d4_rnm3d4,rqLessOrEqual__r1_xreal_0__rn2d3_r0,rqLessOrEqual__r1_xreal_0__rn2d3_r1,rqLessOrEqual__r1_xreal_0__rn2d3_r2,rqLessOrEqual__r1_xreal_0__rn2d3_r3,rqLessOrEqual__r1_xreal_0__rn2d3_r4,rqLessOrEqual__r1_xreal_0__rn2d3_rm1,rqLessOrEqual__r1_xreal_0__rn2d3_rn1d3,rqLessOrEqual__r1_xreal_0__rn2d3_rn2d3,rqLessOrEqual__r1_xreal_0__rn2d3_rnm1d3,rqLessOrEqual__r1_xreal_0__rn3d2_r0,rqLessOrEqual__r1_xreal_0__rn3d2_r1,rqLessOrEqual__r1_xreal_0__rn3d2_r2,rqLessOrEqual__r1_xreal_0__rn3d2_r3,rqLessOrEqual__r1_xreal_0__rn3d2_r4,rqLessOrEqual__r1_xreal_0__rn3d2_rm1,rqLessOrEqual__r1_xreal_0__rn3d2_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d2_rn3d4,rqLessOrEqual__r1_xreal_0__rn3d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rn3d4_r0,rqLessOrEqual__r1_xreal_0__rn3d4_r1,rqLessOrEqual__r1_xreal_0__rn3d4_r2,rqLessOrEqual__r1_xreal_0__rn3d4_r3,rqLessOrEqual__r1_xreal_0__rn3d4_r4,rqLessOrEqual__r1_xreal_0__rn3d4_rm1,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d2,rqLessOrEqual__r1_xreal_0__rn3d4_rn1d4,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d2,rqLessOrEqual__r1_xreal_0__rn3d4_rn3d4,rqLessOrEqual__r1_xreal_0__rn3d4_rnm1d4,rqLessOrEqual__r1_xreal_0__rnm1d2_r0,rqLessOrEqual__r1_xreal_0__rnm1d2_r1,rqLessOrEqual__r1_xreal_0__rnm1d2_r2,rqLessOrEqual__r1_xreal_0__rnm1d2_r4,rqLessOrEqual__r1_xreal_0__rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rn1d4,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d2,rqLessOrEqual__r1_xreal_0__rnm1d2_rnm1d4,rqLessOrEqual__r1_xreal_0__rnm1d3_r0,rqLessOrEqual__r1_xreal_0__rnm1d3_r1,rqLessOrEqual__r1_xreal_0__rnm1d3_r2,rqLessOrEqual__r1_xreal_0__rnm1d3_r3,rqLessOrEqual__r1_xreal_0__rnm1d3_rm1,rqLessOrEqual__r1_xreal_0__rnm1d3_rn1d3,rqLessOrEqual__r1_xreal_0__rnm1d3_rn2d3,rqLessOrEqual__r1_xreal_0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__rn3d4_r4_r3,rqRealMult__k3_xcmplx_0__rn3d4_rm2_rnm3d2,rqRealMult__k3_xcmplx_0__rn3d4_rm4_rm3,rqRealMult__k3_xcmplx_0__rn3d4_rn4d3_r1,rqRealMult__k3_xcmplx_0__rn3d4_rnm4d3_rm1,rqRealMult__k3_xcmplx_0__rn4d3_r1_rn4d3,rqRealMult__k3_xcmplx_0__rn4d3_r3_r4,rqRealMult__k3_xcmplx_0__rn4d3_rn1d4_rn1d3,rqRealMult__k3_xcmplx_0__rn4d3_rn3d4_r1,rqRealMult__k3_xcmplx_0__rn4d3_rnm1d4_rnm1d3,rqRealMult__k3_xcmplx_0__rn4d3_rnm3d4_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2,rqRealMult__k3_xcmplx_0__rnm1d2_r4_rm2,rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm4_r2,rqRealMult__k3_xcmplx_0__rnm1d2_rn1d2_rnm1d4,rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d2_rnm1d2_rn1d4,rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3,rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1,rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3,rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1,rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2,rqRealMult__k3_xcmplx_0__rnm1d4_r1_rnm1d4,rqRealMult__k3_xcmplx_0__rnm1d4_r2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d4_r3_rnm3d4,rqRealMult__k3_xcmplx_0__rnm1d4_r4_rm1,rqRealMult__k3_xcmplx_0__rnm1d4_rm2_rn1d2,rqRealMult__k3_xcmplx_0__rnm1d4_rm3_rn3d4,rqRealMult__k3_xcmplx_0__rnm1d4_rm4_r1,rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3,rqRealMult__k3_xcmplx_0__rnm2d3_r2_rnm4d3,rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2,rqRealMult__k3_xcmplx_0__rnm2d3_rm2_rn4d3,rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2,rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3,rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1,rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3,rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3,rqRealMult__k3_xcmplx_0__rnm3d2_rn1d2_rnm3d4,rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d2_rn4d3_rm2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d2_rn3d4,rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2,rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1,rqRealMult__k3_xcmplx_0__rnm3d2_rnm4d3_r2,rqRealMult__k3_xcmplx_0__rnm3d4_r1_rnm3d4,rqRealMult__k3_xcmplx_0__rnm3d4_r2_rnm3d2,rqRealMult__k3_xcmplx_0__rnm3d4_r4_rm3,rqRealMult__k3_xcmplx_0__rnm3d4_rm2_rn3d2,rqRealMult__k3_xcmplx_0__rnm3d4_rm4_r3,rqRealMult__k3_xcmplx_0__rnm3d4_rn1d3_rnm1d4,rqRealMult__k3_xcmplx_0__rnm3d4_rn4d3_rm1,rqRealMult__k3_xcmplx_0__rnm3d4_rnm4d3_r1,rqRealMult__k3_xcmplx_0__rnm4d3_r1_rnm4d3,rqRealMult__k3_xcmplx_0__rnm4d3_r3_rm4,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d2_rnm2d3,rqRealMult__k3_xcmplx_0__rnm4d3_rn1d4_rnm1d3,rqRealMult__k3_xcmplx_0__rnm4d3_rn3d4_rm1,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d2_rn2d3,rqRealMult__k3_xcmplx_0__rnm4d3_rnm1d4_rn1d3,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d2_r2,rqRealMult__k3_xcmplx_0__rnm4d3_rnm3d4_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__r3_rm3,rqRealNeg__k4_xcmplx_0__r4_rm4,rqRealNeg__k4_xcmplx_0__rm3_r3,rqRealNeg__k4_xcmplx_0__rm4_r4,rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3,rqRealNeg__k4_xcmplx_0__rn1d4_rnm1d4,rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3,rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2,rqRealNeg__k4_xcmplx_0__rn3d4_rnm3d4,rqRealNeg__k4_xcmplx_0__rn4d3_rnm4d3,rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3,rqRealNeg__k4_xcmplx_0__rnm1d4_rn1d4,rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3,rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2,rqRealNeg__k4_xcmplx_0__rnm3d4_rn3d4,rqRealNeg__k4_xcmplx_0__rnm4d3_rn4d3,spc0_numerals,spc1_numerals,spc2_numerals,spc3_numerals,spc4_numerals,spc0_boole,spc1_boole,spc2_boole,spc3_boole,spc4_boole,e23_2_1_2_1__ali2,e2_2_1_2_1__ali2,t21_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__rm2_r2_rm4,rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2,rqRealDiff__k6_xcmplx_0__rm2_r1_rm3,rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqLessOrEqual__r1_xreal_0__r2_r2]),
    [interesting(0.35),file(ali2,e24_2_1_2_1__ali2),[file(ali2,e24_2_1_2_1__ali2)]]).

fof(e25_2_1_2_1__ali2,plain,(
    ~ r2_hidden(c4_2_1_2_1__ali2,c1_2_1_2__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc1_xreal_0,fc4_subset_1,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_l1_pre_topc,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_k5_pcomps_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,dt_c3_2_1_2_1__ali2,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc2_membered,fc3_pcomps_1,fc4_pcomps_1,fc4_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,dt_c2_2__ali2,dt_c2_2_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,dt_c4_2_1_2_1__ali2,de_c4_2_1_2_1__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e24_2_1_2_1__ali2,e3_2_1_2__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e25_2_1_2_1__ali2),[file(ali2,e25_2_1_2_1__ali2)]]).

fof(t50_subset_1,theorem,(
    ! [A] : 
      ( A != k1_xboole_0
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ( ~ r2_hidden(C,B)
               => r2_hidden(C,k3_subset_1(A,B)) ) ) ) ) ),
    file(subset_1,t50_subset_1),
    [interesting(0.9),axiom,file(subset_1,t50_subset_1)]).

fof(e26_2_1_2_1__ali2,plain,(
    r2_hidden(c3_2_1_2_1__ali2,c3_2_1_2__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t8_boole,free_g1_pre_topc,involutiveness_k3_subset_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_g1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,dt_c3_2_1_2__ali2,dt_c3_2_1_2_1__ali2,dt_c4_2_1_2_1__ali2,de_c3_2_1_2__ali2,de_c4_2_1_2_1__ali2,fc1_subset_1,fc6_membered,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e25_2_1_2_1__ali2,e4_2_1_2__ali2,t50_subset_1]),
    [interesting(0.35),file(ali2,e26_2_1_2_1__ali2),[file(ali2,e26_2_1_2_1__ali2)]]).

fof(i7_2_1_2_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i7_2_1_2_1__ali2)]),
    [interesting(0.35),trivial,file(ali2,i7_2_1_2_1__ali2)]).

fof(i6_2_1_2_1__ali2,plain,(
    r2_hidden(c3_2_1_2_1__ali2,c3_2_1_2__ali2) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_2_1_2_1__ali2,e7_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e26_2_1_2_1__ali2,i7_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,i6_2_1_2_1__ali2),[file(ali2,i6_2_1_2_1__ali2)]]).

fof(i5_2_1_2_1__ali2,plain,(
    ~ ( r2_hidden(c3_2_1_2_1__ali2,k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2))
      & ~ r2_hidden(c3_2_1_2_1__ali2,c3_2_1_2__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e7_2_1_2_1__ali2])],[e7_2_1_2_1__ali2,i6_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,i5_2_1_2_1__ali2),[file(ali2,i5_2_1_2_1__ali2)]]).

fof(i5_2_1_2_1_tmp__ali2,plain,(
    ~ ( r2_hidden(c3_2_1_2_1__ali2,k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2))
      & ~ r2_hidden(c3_2_1_2_1__ali2,c3_2_1_2__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c3_2_1_2_1__ali2])],[dt_c3_2_1_2_1__ali2,i5_2_1_2_1__ali2]),
    [interesting(0.35),i4_2_1_2_1__ali2]).

fof(i4_2_1_2_1__ali2,plain,(
    r1_tarski(k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2),c3_2_1_2__ali2) ),
    inference(let,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[i5_2_1_2_1_tmp__ali2,cc1_xreal_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_l1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc7_xreal_0,fc1_struct_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,cc2_xreal_0,cc6_membered,fc1_subset_1,fc2_membered,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k9_metric_1,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2_1_2__ali2,d3_tarski,dh_c3_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,i4_2_1_2_1__ali2),[file(ali2,i4_2_1_2_1__ali2)]]).

fof(i3_2_1_2_1__ali2,plain,
    ( ~ r1_xreal_0(c2_2_1_2_1__ali2,0)
    & r1_tarski(k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,c2_2_1_2_1__ali2),c3_2_1_2__ali2) ),
    inference(conclusion,[status(thm),assumptions([e1_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e6_2_1_2_1__ali2,i4_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,i3_2_1_2_1__ali2),[file(ali2,i3_2_1_2_1__ali2)]]).

fof(i2_2_1_2_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ~ r1_xreal_0(A,0)
      & r1_tarski(k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,A),c3_2_1_2__ali2) ) ),
    inference(take,[status(thm),assumptions([e1_2_1_2_1__ali2,dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc1_xreal_0,dt_k5_ordinal2,dt_l1_struct_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_struct_0,fc5_membered,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_struct_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_metric_1,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_k1_numbers,dt_k9_metric_1,dt_m1_subset_1,dt_c1_2__ali2,dt_c1_2_1_2_1__ali2,dt_c2_2_1_2_1__ali2,dt_c3_2_1_2__ali2,fc2_membered,spc0_numerals,spc0_boole,i3_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,i2_2_1_2_1__ali2),[file(ali2,i2_2_1_2_1__ali2)]]).

fof(i1_2_1_2_1__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_2_1__ali2,c3_2_1_2__ali2)
      & ! [A] : 
          ( m1_subset_1(A,k1_numbers)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_tarski(k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,A),c3_2_1_2__ali2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_2_1__ali2,dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e1_2_1_2_1__ali2])],[e1_2_1_2_1__ali2,i2_2_1_2_1__ali2]),
    [interesting(0.35),file(ali2,i1_2_1_2_1__ali2),[file(ali2,i1_2_1_2_1__ali2)]]).

fof(i1_2_1_2_1_tmp__ali2,plain,
    ( m1_subset_1(c1_2_1_2_1__ali2,u1_struct_0(c1_2__ali2))
   => ~ ( r2_hidden(c1_2_1_2_1__ali2,c3_2_1_2__ali2)
        & ! [A] : 
            ( m1_subset_1(A,k1_numbers)
           => ~ ( ~ r1_xreal_0(A,0)
                & r1_tarski(k9_metric_1(c1_2__ali2,c1_2_1_2_1__ali2,A),c3_2_1_2__ali2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_2_1__ali2])],[dt_c1_2_1_2_1__ali2,i1_2_1_2_1__ali2]),
    [interesting(0.5),e6_2_1_2__ali2]).

fof(e6_2_1_2__ali2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
     => ~ ( r2_hidden(A,c3_2_1_2__ali2)
          & ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ~ ( ~ r1_xreal_0(B,0)
                  & r1_tarski(k9_metric_1(c1_2__ali2,A,B),c3_2_1_2__ali2) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[i1_2_1_2_1_tmp__ali2,dh_c1_2_1_2_1__ali2]),
    [interesting(0.5),file(ali2,e6_2_1_2__ali2),[file(ali2,e6_2_1_2__ali2)]]).

fof(d5_pcomps_1,definition,(
    ! [A] : 
      ( l1_metric_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( B = k4_pcomps_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                <=> ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( m1_subset_1(E,k1_numbers)
                             => ~ ( ~ r1_xreal_0(E,0)
                                  & r1_tarski(k9_metric_1(A,D,E),C) ) ) ) ) ) ) ) ) ) ),
    file(pcomps_1,d5_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,d5_pcomps_1)]).

fof(e7_2_1_2__ali2,plain,(
    r2_hidden(k3_subset_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1_2__ali2),k4_pcomps_1(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc1_xreal_0,free_g1_pre_topc,dt_g1_pre_topc,dt_k1_xboole_0,dt_k5_ordinal2,dt_u1_pre_topc,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_struct_0,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_numerals,t1_real,t2_subset,t4_real,t5_subset,t6_boole,t8_boole,involutiveness_k3_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_l1_metric_1,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_k9_metric_1,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,dt_c3_2_1_2__ali2,de_c3_2_1_2__ali2,cc6_membered,fc1_subset_1,fc2_membered,fc3_pcomps_1,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t3_subset,t4_subset,t7_boole,spc0_numerals,spc0_boole,e6_2_1_2__ali2,d5_pcomps_1]),
    [interesting(0.5),file(ali2,e7_2_1_2__ali2),[file(ali2,e7_2_1_2__ali2)]]).

fof(d5_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> r2_hidden(B,u1_pre_topc(A)) ) ) ) ),
    file(pre_topc,d5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,d5_pre_topc)]).

fof(e8_2_1_2__ali2,plain,(
    v3_pre_topc(k3_subset_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1_2__ali2),k5_pcomps_1(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_metric_1,existence_l1_struct_0,dt_l1_metric_1,dt_l1_struct_0,cc15_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,free_g1_pre_topc,involutiveness_k3_subset_1,antisymmetry_r2_hidden,existence_l1_pre_topc,existence_m1_subset_1,dt_g1_pre_topc,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_pre_topc,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e7_2_1_2__ali2,e4_2_1_2__ali2,d5_pre_topc]),
    [interesting(0.5),file(ali2,e8_2_1_2__ali2),[file(ali2,e8_2_1_2__ali2)]]).

fof(t29_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_pre_topc(B,A)
          <=> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_1,t29_tops_1),
    [interesting(0.9),axiom,file(tops_1,t29_tops_1)]).

fof(e9_2_1_2__ali2,plain,(
    v4_pre_topc(c1_2_1_2__ali2,k5_pcomps_1(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,abstractness_v1_pre_topc,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_metric_1,existence_l1_struct_0,dt_l1_metric_1,dt_l1_struct_0,cc15_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,involutiveness_k3_subset_1,existence_l1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k5_pcomps_1,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_2__ali2,fc1_subset_1,t3_subset,e8_2_1_2__ali2,t29_tops_1]),
    [interesting(0.5),file(ali2,e9_2_1_2__ali2),[file(ali2,e9_2_1_2__ali2)]]).

fof(i3_2_1_2__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i3_2_1_2__ali2)]),
    [interesting(0.5),trivial,file(ali2,i3_2_1_2__ali2)]).

fof(i2_2_1_2__ali2,plain,(
    v4_pre_topc(c1_2_1_2__ali2,k5_pcomps_1(c1_2__ali2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1_2__ali2,e1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e9_2_1_2__ali2,i3_2_1_2__ali2]),
    [interesting(0.5),file(ali2,i2_2_1_2__ali2),[file(ali2,i2_2_1_2__ali2)]]).

fof(i1_2_1_2__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_2__ali2,c1_2_1__ali2)
      & ~ v4_pre_topc(c1_2_1_2__ali2,k5_pcomps_1(c1_2__ali2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e1_2_1_2__ali2])],[e1_2_1_2__ali2,i2_2_1_2__ali2]),
    [interesting(0.5),file(ali2,i1_2_1_2__ali2),[file(ali2,i1_2_1_2__ali2)]]).

fof(i1_2_1_2_tmp__ali2,plain,
    ( m1_subset_1(c1_2_1_2__ali2,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(c1_2__ali2))))
   => ~ ( r2_hidden(c1_2_1_2__ali2,c1_2_1__ali2)
        & ~ v4_pre_topc(c1_2_1_2__ali2,k5_pcomps_1(c1_2__ali2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_2__ali2])],[dt_c1_2_1_2__ali2,i1_2_1_2__ali2]),
    [interesting(0.65),e7_2_1__ali2]).

fof(e7_2_1__ali2,plain,(
    v2_tops_2(c1_2_1__ali2,k5_pcomps_1(c1_2__ali2)) ),
    inference(let,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[i1_2_1_2_tmp__ali2,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,abstractness_v1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,dt_l1_metric_1,dt_l1_struct_0,cc15_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k5_pcomps_1,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,fc1_subset_1,d2_tops_2,dh_c1_2_1_2__ali2]),
    [interesting(0.65),file(ali2,e7_2_1__ali2),[file(ali2,e7_2_1__ali2)]]).

fof(d2_compts_1,definition,(
    ! [A] : 
      ( v1_compts_1(A)
    <=> ( A != k1_xboole_0
        & ! [B] : 
            ~ ( B != k1_xboole_0
              & r1_tarski(B,A)
              & v1_finset_1(B)
              & k1_setfam_1(B) = k1_xboole_0 ) ) ) ),
    file(compts_1,d2_compts_1),
    [interesting(0.9),axiom,file(compts_1,d2_compts_1)]).

fof(commutativity_k1_nat_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(redefinition_k1_nat_1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    [interesting(0.9),axiom,file(nat_1,k1_nat_1)]).

fof(fraenkel_a_4_0_ali2,definition,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(B)
        & v6_metric_1(B)
        & v7_metric_1(B)
        & v8_metric_1(B)
        & v9_metric_1(B)
        & l1_metric_1(B)
        & m1_ali2(C,B)
        & m1_subset_1(D,k1_numbers)
        & m1_subset_1(E,u1_struct_0(B)) )
     => ( r2_hidden(A,a_4_0_ali2(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,u1_struct_0(B))
            & A = F
            & r1_xreal_0(k4_metric_1(B,F,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,F)),k4_real_1(k4_metric_1(B,E,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E)),k4_power(D,k1_nat_1(0,1)))) ) ) ) ),
    file(ali2,a_4_0_ali2),
    [interesting(0.9),axiom,file(ali2,a_4_0_ali2)]).

fof(e4_2_1__ali2,plain,(
    k5_pcomps_1(c1_2__ali2) = g1_pre_topc(u1_struct_0(c1_2__ali2),k4_pcomps_1(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc3_xreal_0,fc8_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,dt_u1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc5_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_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_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc2_membered,fc4_pcomps_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc6_arithm,t1_arithm,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,free_g1_pre_topc,commutativity_k2_xcmplx_0,existence_l1_metric_1,dt_g1_pre_topc,dt_k2_xcmplx_0,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_l1_metric_1,dt_u1_struct_0,dt_c1_2__ali2,fc3_pcomps_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d6_pcomps_1,rqRealAdd__k2_xcmplx_0__r0_r1_r1]),
    [interesting(0.65),file(ali2,e4_2_1__ali2),[file(ali2,e4_2_1__ali2)]]).

fof(s7_domain_1__e5_2_1__ali2,theorem,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A)
        & m1_ali2(B,A)
        & m1_subset_1(C,k1_numbers)
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(a_4_0_ali2(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(ali2,s7_domain_1__e5_2_1__ali2),
    [interesting(0.9),axiom,file(ali2,s7_domain_1__e5_2_1__ali2)]).

fof(e5_2_1__ali2,plain,(
    m1_subset_1(a_4_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2),k1_zfmisc_1(u1_struct_0(c1_2__ali2))) ),
    inference(mizar_from,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[dt_k5_ordinal2,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_power,dt_k3_xcmplx_0,dt_k5_numbers,dt_m1_relset_1,dt_m2_subset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc23_xreal_0,fc3_xreal_0,fc4_subset_1,fc4_xreal_0,fc8_xreal_0,rc1_membered,rc1_xreal_0,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_nat_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_l1_struct_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,dt_k1_numbers,dt_k1_zfmisc_1,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,fc1_subset_1,fc2_membered,t2_tarski,fraenkel_a_4_0_ali2,s7_domain_1__e5_2_1__ali2]),
    [interesting(0.65),file(ali2,e5_2_1__ali2),[file(ali2,e5_2_1__ali2)]]).

fof(e1_2_1_1__ali2,plain,(
    c1_2_1__ali2 != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[dt_k2_zfmisc_1,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,fc4_subset_1,fc7_xreal_0,fc9_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_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k3_power,dt_m1_relset_1,dt_m2_relset_1,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_xreal_0,t1_real,t4_real,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,abstractness_v1_pre_topc,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k1_nat_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t2_arithm,t2_subset,t3_arithm,t5_subset,t8_boole,free_g1_pre_topc,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_g1_pre_topc,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k4_pcomps_1,dt_k5_numbers,dt_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,fc6_membered,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,t1_numerals,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,t2_tarski,fraenkel_a_4_0_ali2,fraenkel_a_5_0_ali2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_2_1__ali2,e4_2_1__ali2,e5_2_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1]),
    [interesting(0.5),file(ali2,e1_2_1_1__ali2),[file(ali2,e1_2_1_1__ali2)]]).

fof(dh_c1_2_1_1__ali2,definition,
    ( ~ ( c1_2_1_1__ali2 != k1_xboole_0
        & r1_tarski(c1_2_1_1__ali2,c1_2_1__ali2)
        & v1_finset_1(c1_2_1_1__ali2)
        & k1_setfam_1(c1_2_1_1__ali2) = k1_xboole_0 )
   => ! [A] : 
        ~ ( A != k1_xboole_0
          & r1_tarski(A,c1_2_1__ali2)
          & v1_finset_1(A)
          & k1_setfam_1(A) = k1_xboole_0 ) ),
    introduced(definition,[new_symbol(c1_2_1_1__ali2),file(ali2,c1_2_1_1__ali2)]),
    [interesting(0.5),axiom,file(ali2,c1_2_1_1__ali2)]).

fof(e2_2_1_1__ali2,assumption,(
    c1_2_1_1__ali2 != k1_xboole_0 ),
    introduced(assumption,[file(ali2,e2_2_1_1__ali2)]),
    [interesting(0.5),axiom,file(ali2,e2_2_1_1__ali2)]).

fof(e3_2_1_1__ali2,assumption,(
    r1_tarski(c1_2_1_1__ali2,c1_2_1__ali2) ),
    introduced(assumption,[file(ali2,e3_2_1_1__ali2)]),
    [interesting(0.5),axiom,file(ali2,e3_2_1_1__ali2)]).

fof(e4_2_1_1__ali2,assumption,(
    v1_finset_1(c1_2_1_1__ali2) ),
    introduced(assumption,[file(ali2,e4_2_1_1__ali2)]),
    [interesting(0.5),axiom,file(ali2,e4_2_1_1__ali2)]).

fof(dt_c1_2_1_1__ali2,assumption,(
    $true ),
    introduced(assumption,[file(ali2,c1_2_1_1__ali2)]),
    [interesting(0.5),axiom,file(ali2,c1_2_1_1__ali2)]).

fof(dh_c2_2_1_1__ali2,definition,
    ( ? [A] : 
        ( r2_hidden(A,c1_2_1_1__ali2)
        & ! [B] : 
            ( r2_hidden(B,c1_2_1_1__ali2)
           => r1_tarski(A,B) ) )
   => ( r2_hidden(c2_2_1_1__ali2,c1_2_1_1__ali2)
      & ! [C] : 
          ( r2_hidden(C,c1_2_1_1__ali2)
         => r1_tarski(c2_2_1_1__ali2,C) ) ) ),
    introduced(definition,[new_symbol(c2_2_1_1__ali2),file(ali2,c2_2_1_1__ali2)]),
    [interesting(0.5),axiom,file(ali2,c2_2_1_1__ali2)]).

fof(symmetry_r3_xboole_0,theorem,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
     => r3_xboole_0(B,A) ) ),
    file(xboole_0,r3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r3_xboole_0)]).

fof(reflexivity_r3_xboole_0,theorem,(
    ! [A,B] : r3_xboole_0(A,A) ),
    file(xboole_0,r3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r3_xboole_0)]).

fof(dt_c1_2_1_1_1__ali2,assumption,(
    $true ),
    introduced(assumption,[file(ali2,c1_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c1_2_1_1_1__ali2)]).

fof(dt_c2_2_1_1_1__ali2,assumption,(
    $true ),
    introduced(assumption,[file(ali2,c2_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c2_2_1_1_1__ali2)]).

fof(d9_ordinal1,definition,(
    ! [A] : 
      ( v6_ordinal1(A)
    <=> ! [B,C] : 
          ( ( r2_hidden(B,A)
            & r2_hidden(C,A) )
         => r3_xboole_0(B,C) ) ) ),
    file(ordinal1,d9_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,d9_ordinal1)]).

fof(dh_c1_2_1_1_1__ali2,definition,
    ( ! [A] : 
        ~ ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1_1__ali2)
          & r2_hidden(A,c1_2_1_1__ali2)
          & ~ r3_xboole_0(c1_2_1_1_1__ali2,A) )
   => ! [B,C] : 
        ~ ( r2_hidden(B,c1_2_1_1__ali2)
          & r2_hidden(C,c1_2_1_1__ali2)
          & ~ r3_xboole_0(B,C) ) ),
    introduced(definition,[new_symbol(c1_2_1_1_1__ali2),file(ali2,c1_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c1_2_1_1_1__ali2)]).

fof(dh_c2_2_1_1_1__ali2,definition,
    ( ~ ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1_1__ali2)
        & r2_hidden(c2_2_1_1_1__ali2,c1_2_1_1__ali2)
        & ~ r3_xboole_0(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) )
   => ! [A] : 
        ~ ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1_1__ali2)
          & r2_hidden(A,c1_2_1_1__ali2)
          & ~ r3_xboole_0(c1_2_1_1_1__ali2,A) ) ),
    introduced(definition,[new_symbol(c2_2_1_1_1__ali2),file(ali2,c2_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c2_2_1_1_1__ali2)]).

fof(e1_2_1_1_1__ali2,assumption,
    ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1_1__ali2)
    & r2_hidden(c2_2_1_1_1__ali2,c1_2_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,e1_2_1_1_1__ali2)]).

fof(d9_xboole_0,definition,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        | r1_tarski(B,A) ) ) ),
    file(xboole_0,d9_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d9_xboole_0)]).

fof(dh_c3_2_1_1_1__ali2,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & c1_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) )
   => ( m2_subset_1(c3_2_1_1_1__ali2,k1_numbers,k5_numbers)
      & c1_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c3_2_1_1_1__ali2) ) ),
    introduced(definition,[new_symbol(c3_2_1_1_1__ali2),file(ali2,c3_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c3_2_1_1_1__ali2)]).

fof(e2_2_1_1_1__ali2,plain,
    ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1__ali2)
    & r2_hidden(c2_2_1_1_1__ali2,c1_2_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,abstractness_v1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_xboole_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc6_membered,rc1_membered,rc3_struct_0,rc5_struct_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,cc15_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,t1_subset,t3_subset,t7_boole,e1_2_1_1_1__ali2,e3_2_1_1__ali2]),
    [interesting(0.35),file(ali2,e2_2_1_1_1__ali2),[file(ali2,e2_2_1_1_1__ali2)]]).

fof(e3_2_1_1_1__ali2,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & c1_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,abstractness_v1_pre_topc,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_xreal_0,fc6_membered,rc1_xreal_0,spc7_arithm,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,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_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t1_subset,t3_subset,t4_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,e2_2_1_1_1__ali2,e3_2_1__ali2]),
    [interesting(0.35),file(ali2,e3_2_1_1_1__ali2),[file(ali2,e3_2_1_1_1__ali2)]]).

fof(dt_c3_2_1_1_1__ali2,plain,(
    m2_subset_1(c3_2_1_1_1__ali2,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c3_2_1_1_1__ali2,e3_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,c3_2_1_1_1__ali2),[file(ali2,c3_2_1_1_1__ali2)]]).

fof(dh_c4_2_1_1_1__ali2,definition,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & c2_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) )
   => ( m2_subset_1(c4_2_1_1_1__ali2,k1_numbers,k5_numbers)
      & c2_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c4_2_1_1_1__ali2) ) ),
    introduced(definition,[new_symbol(c4_2_1_1_1__ali2),file(ali2,c4_2_1_1_1__ali2)]),
    [interesting(0.35),axiom,file(ali2,c4_2_1_1_1__ali2)]).

fof(e5_2_1_1_1__ali2,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & c2_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,abstractness_v1_pre_topc,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_xreal_0,fc6_membered,rc1_xreal_0,spc7_arithm,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,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_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t1_subset,t3_subset,t4_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,e3_2_1__ali2,e2_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,e5_2_1_1_1__ali2),[file(ali2,e5_2_1_1_1__ali2)]]).

fof(dt_c4_2_1_1_1__ali2,plain,(
    m2_subset_1(c4_2_1_1_1__ali2,k1_numbers,k5_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[dh_c4_2_1_1_1__ali2,e5_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,c4_2_1_1_1__ali2),[file(ali2,c4_2_1_1_1__ali2)]]).

fof(e1_2_1_1_1_3_1_1__ali2,assumption,(
    r1_xreal_0(c3_2_1_1_1__ali2,c4_2_1_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_3_1_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,e1_2_1_1_1_3_1_1__ali2)]).

fof(dt_c1_2_1_1_1_3_1_1_1__ali2,assumption,(
    $true ),
    introduced(assumption,[file(ali2,c1_2_1_1_1_3_1_1_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,c1_2_1_1_1_3_1_1_1__ali2)]).

fof(dh_c1_2_1_1_1_3_1_1_1__ali2,definition,
    ( ~ ( r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c2_2_1_1_1__ali2)
        & ~ r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c1_2_1_1_1__ali2) )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_2_1_1_1__ali2)
          & ~ r2_hidden(A,c1_2_1_1_1__ali2) ) ),
    introduced(definition,[new_symbol(c1_2_1_1_1_3_1_1_1__ali2),file(ali2,c1_2_1_1_1_3_1_1_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,c1_2_1_1_1_3_1_1_1__ali2)]).

fof(e1_2_1_1_1_3_1_1_1__ali2,assumption,(
    r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c2_2_1_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_3_1_1_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,e1_2_1_1_1_3_1_1_1__ali2)]).

fof(dh_c2_2_1_1_1_3_1_1_1__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
        & c1_2_1_1_1_3_1_1_1__ali2 = A
        & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2))) )
   => ( m1_subset_1(c2_2_1_1_1_3_1_1_1__ali2,u1_struct_0(c1_2__ali2))
      & c1_2_1_1_1_3_1_1_1__ali2 = c2_2_1_1_1_3_1_1_1__ali2
      & r1_xreal_0(k4_metric_1(c1_2__ali2,c2_2_1_1_1_3_1_1_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c2_2_1_1_1_3_1_1_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2))) ) ),
    introduced(definition,[new_symbol(c2_2_1_1_1_3_1_1_1__ali2),file(ali2,c2_2_1_1_1_3_1_1_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,c2_2_1_1_1_3_1_1_1__ali2)]).

fof(e6_2_1_1_1__ali2,plain,(
    c2_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c4_2_1_1_1__ali2) ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[dh_c4_2_1_1_1__ali2,e5_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,e6_2_1_1_1__ali2),[file(ali2,e6_2_1_1_1__ali2)]]).

fof(e2_2_1_1_1_3_1_1_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & c1_2_1_1_1_3_1_1_1__ali2 = A
      & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,dt_c4_2_1_1_1__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e1_2_1_1_1_3_1_1_1__ali2,e6_2_1_1_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e2_2_1_1_1_3_1_1_1__ali2),[file(ali2,e2_2_1_1_1_3_1_1_1__ali2)]]).

fof(dt_c2_2_1_1_1_3_1_1_1__ali2,plain,(
    m1_subset_1(c2_2_1_1_1_3_1_1_1__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[dh_c2_2_1_1_1_3_1_1_1__ali2,e2_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),file(ali2,c2_2_1_1_1_3_1_1_1__ali2),[file(ali2,c2_2_1_1_1_3_1_1_1__ali2)]]).

fof(dh_c1_2_1_1_1_2__ali2,definition,
    ( ( m2_subset_1(c1_2_1_1_1_2__ali2,k1_numbers,k5_numbers)
     => ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r1_xreal_0(c1_2_1_1_1_2__ali2,A)
           => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ) ) )
   => ! [B] : 
        ( m2_subset_1(B,k1_numbers,k5_numbers)
       => ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ( r1_xreal_0(B,C)
             => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,C)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,B))) ) ) ) ),
    introduced(definition,[new_symbol(c1_2_1_1_1_2__ali2),file(ali2,c1_2_1_1_1_2__ali2)]),
    [interesting(0.2),axiom,file(ali2,c1_2_1_1_1_2__ali2)]).

fof(dh_c2_2_1_1_1_2__ali2,definition,
    ( ( m2_subset_1(c2_2_1_1_1_2__ali2,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c1_2_1_1_1_2__ali2,c2_2_1_1_1_2__ali2)
       => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_1_1_2__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r1_xreal_0(c1_2_1_1_1_2__ali2,A)
         => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ) ) ),
    introduced(definition,[new_symbol(c2_2_1_1_1_2__ali2),file(ali2,c2_2_1_1_1_2__ali2)]),
    [interesting(0.2),axiom,file(ali2,c2_2_1_1_1_2__ali2)]).

fof(e1_2_1_1_1_2__ali2,assumption,(
    r1_xreal_0(c1_2_1_1_1_2__ali2,c2_2_1_1_1_2__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_2__ali2)]),
    [interesting(0.2),axiom,file(ali2,e1_2_1_1_1_2__ali2)]).

fof(dt_c1_2_1_1_1_2__ali2,assumption,(
    m2_subset_1(c1_2_1_1_1_2__ali2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(ali2,c1_2_1_1_1_2__ali2)]),
    [interesting(0.2),axiom,file(ali2,c1_2_1_1_1_2__ali2)]).

fof(dt_c2_2_1_1_1_2__ali2,assumption,(
    m2_subset_1(c2_2_1_1_1_2__ali2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(ali2,c2_2_1_1_1_2__ali2)]),
    [interesting(0.2),axiom,file(ali2,c2_2_1_1_1_2__ali2)]).

fof(dh_c1_2_1_1_1_1__ali2,definition,
    ( ( m2_subset_1(c1_2_1_1_1_1__ali2,k1_numbers,k5_numbers)
     => ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r1_xreal_0(c1_2_1_1_1_1__ali2,A)
           => r1_xreal_0(k4_power(c3_2__ali2,A),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ) ) )
   => ! [B] : 
        ( m2_subset_1(B,k1_numbers,k5_numbers)
       => ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ( r1_xreal_0(B,C)
             => r1_xreal_0(k4_power(c3_2__ali2,C),k4_power(c3_2__ali2,B)) ) ) ) ),
    introduced(definition,[new_symbol(c1_2_1_1_1_1__ali2),file(ali2,c1_2_1_1_1_1__ali2)]),
    [interesting(0.2),axiom,file(ali2,c1_2_1_1_1_1__ali2)]).

fof(dh_c2_2_1_1_1_1__ali2,definition,
    ( ( m2_subset_1(c2_2_1_1_1_1__ali2,k1_numbers,k5_numbers)
     => ( r1_xreal_0(c1_2_1_1_1_1__ali2,c2_2_1_1_1_1__ali2)
       => r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r1_xreal_0(c1_2_1_1_1_1__ali2,A)
         => r1_xreal_0(k4_power(c3_2__ali2,A),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ) ) ),
    introduced(definition,[new_symbol(c2_2_1_1_1_1__ali2),file(ali2,c2_2_1_1_1_1__ali2)]),
    [interesting(0.2),axiom,file(ali2,c2_2_1_1_1_1__ali2)]).

fof(e1_2_1_1_1_1__ali2,assumption,(
    r1_xreal_0(c1_2_1_1_1_1__ali2,c2_2_1_1_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_1__ali2)]),
    [interesting(0.2),axiom,file(ali2,e1_2_1_1_1_1__ali2)]).

fof(e1_2_1_1_1_1_1_1__ali2,assumption,(
    ~ r1_xreal_0(c2_2_1_1_1_1__ali2,c1_2_1_1_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_1_1_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,e1_2_1_1_1_1_1_1__ali2)]).

fof(dt_c1_2_1_1_1_1__ali2,assumption,(
    m2_subset_1(c1_2_1_1_1_1__ali2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(ali2,c1_2_1_1_1_1__ali2)]),
    [interesting(0.2),axiom,file(ali2,c1_2_1_1_1_1__ali2)]).

fof(dt_c2_2_1_1_1_1__ali2,assumption,(
    m2_subset_1(c2_2_1_1_1_1__ali2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(ali2,c2_2_1_1_1_1__ali2)]),
    [interesting(0.2),axiom,file(ali2,c2_2_1_1_1_1__ali2)]).

fof(t45_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,0)
                  & ~ r1_xreal_0(1,C)
                  & r1_xreal_0(k3_power(C,A),k3_power(C,B)) ) ) ) ) ),
    file(power,t45_power),
    [interesting(0.9),axiom,file(power,t45_power)]).

fof(e2_2_1_1_1_1_1_1__ali2,plain,(
    r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,e1_2_1_1_1_1_1_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,cc1_xreal_0,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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,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,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_membered,rc1_xreal_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_power,dt_k3_power,dt_k4_power,dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,dt_c3_2__ali2,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_2_1_1_1_1_1_1__ali2,e2_2__ali2,t45_power,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.02),file(ali2,e2_2_1_1_1_1_1_1__ali2),[file(ali2,e2_2_1_1_1_1_1_1__ali2)]]).

fof(i2_2_1_1_1_1_1_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i2_2_1_1_1_1_1_1__ali2)]),
    [interesting(0.02),trivial,file(ali2,i2_2_1_1_1_1_1_1__ali2)]).

fof(i1_2_1_1_1_1_1_1__ali2,plain,(
    r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,e1_2_1_1_1_1_1_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[e2_2_1_1_1_1_1_1__ali2,i2_2_1_1_1_1_1_1__ali2]),
    [interesting(0.02),file(ali2,i1_2_1_1_1_1_1_1__ali2),[file(ali2,i1_2_1_1_1_1_1_1__ali2)]]).

fof(i1_2_1_1_1_1_1__ali2,plain,
    ( ~ r1_xreal_0(c2_2_1_1_1_1__ali2,c1_2_1_1_1_1__ali2)
   => r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2]),discharge_asm(discharge,[e1_2_1_1_1_1_1_1__ali2])],[e1_2_1_1_1_1_1_1__ali2,i1_2_1_1_1_1_1_1__ali2]),
    [interesting(0.05),file(ali2,i1_2_1_1_1_1_1__ali2),[file(ali2,i1_2_1_1_1_1_1__ali2)]]).

fof(e1_2_1_1_1_1_1_2__ali2,assumption,(
    c1_2_1_1_1_1__ali2 = c2_2_1_1_1_1__ali2 ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_1_1_2__ali2)]),
    [interesting(0.02),axiom,file(ali2,e1_2_1_1_1_1_1_2__ali2)]).

fof(e2_2_1_1_1_1_1_2__ali2,plain,(
    r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2,e1_2_1_1_1_1_1_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_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,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_power,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc2_xreal_0,fc2_membered,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_power,dt_k4_power,dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,dt_c3_2__ali2,e1_2_1_1_1_1_1_2__ali2]),
    [interesting(0.02),file(ali2,e2_2_1_1_1_1_1_2__ali2),[file(ali2,e2_2_1_1_1_1_1_2__ali2)]]).

fof(i2_2_1_1_1_1_1_2__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i2_2_1_1_1_1_1_2__ali2)]),
    [interesting(0.02),trivial,file(ali2,i2_2_1_1_1_1_1_2__ali2)]).

fof(i1_2_1_1_1_1_1_2__ali2,plain,(
    r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2,e1_2_1_1_1_1_1_2__ali2])],[e2_2_1_1_1_1_1_2__ali2,i2_2_1_1_1_1_1_2__ali2]),
    [interesting(0.02),file(ali2,i1_2_1_1_1_1_1_2__ali2),[file(ali2,i1_2_1_1_1_1_1_2__ali2)]]).

fof(i2_2_1_1_1_1_1__ali2,plain,
    ( c1_2_1_1_1_1__ali2 = c2_2_1_1_1_1__ali2
   => r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,dt_c1_2__ali2,dt_c2_2__ali2]),discharge_asm(discharge,[e1_2_1_1_1_1_1_2__ali2])],[e1_2_1_1_1_1_1_2__ali2,i1_2_1_1_1_1_1_2__ali2]),
    [interesting(0.05),file(ali2,i2_2_1_1_1_1_1__ali2),[file(ali2,i2_2_1_1_1_1_1__ali2)]]).

fof(d5_real_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> ~ ( r1_xreal_0(B,A)
                & B != A ) ) ) ) ),
    file(real_1,d5_real_1),
    [interesting(0.9),axiom,file(real_1,d5_real_1)]).

fof(e1_2_1_1_1_1_1__ali2,plain,(
    ~ ( r1_xreal_0(c2_2_1_1_1_1__ali2,c1_2_1_1_1_1__ali2)
      & c1_2_1_1_1_1__ali2 != c2_2_1_1_1_1__ali2 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,e1_2_1_1_1_1__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_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,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_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_numbers,dt_m2_subset_1,fc2_membered,rc1_xreal_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,cc2_xreal_0,e1_2_1_1_1_1__ali2,d5_real_1]),
    [interesting(0.05),file(ali2,e1_2_1_1_1_1_1__ali2),[file(ali2,e1_2_1_1_1_1_1__ali2)]]).

fof(i2_2_1_1_1_1__ali2,plain,(
    r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(percases,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2,dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,e1_2_1_1_1_1__ali2])],[i1_2_1_1_1_1_1__ali2,i2_2_1_1_1_1_1__ali2,e1_2_1_1_1_1_1__ali2]),
    [interesting(0.2),file(ali2,i2_2_1_1_1_1__ali2),[file(ali2,i2_2_1_1_1_1__ali2)]]).

fof(i1_2_1_1_1_1__ali2,plain,
    ( r1_xreal_0(c1_2_1_1_1_1__ali2,c2_2_1_1_1_1__ali2)
   => r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2,dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2]),discharge_asm(discharge,[e1_2_1_1_1_1__ali2])],[e1_2_1_1_1_1__ali2,i2_2_1_1_1_1__ali2]),
    [interesting(0.2),file(ali2,i1_2_1_1_1_1__ali2),[file(ali2,i1_2_1_1_1_1__ali2)]]).

fof(i1_2_1_1_1_1_tmp__ali2,plain,
    ( ( m2_subset_1(c1_2_1_1_1_1__ali2,k1_numbers,k5_numbers)
      & m2_subset_1(c2_2_1_1_1_1__ali2,k1_numbers,k5_numbers) )
   => ( r1_xreal_0(c1_2_1_1_1_1__ali2,c2_2_1_1_1_1__ali2)
     => r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_1__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_1__ali2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2])],[dt_c1_2_1_1_1_1__ali2,dt_c2_2_1_1_1_1__ali2,i1_2_1_1_1_1__ali2]),
    [interesting(0.35),e7_2_1_1_1__ali2]).

fof(e7_2_1_1_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => r1_xreal_0(k4_power(c3_2__ali2,B),k4_power(c3_2__ali2,A)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[i1_2_1_1_1_1_tmp__ali2,dh_c1_2_1_1_1_1__ali2,dh_c2_2_1_1_1_1__ali2]),
    [interesting(0.35),file(ali2,e7_2_1_1_1__ali2),[file(ali2,e7_2_1_1_1__ali2)]]).

fof(e3_2_1_1_1_2__ali2,plain,(
    r1_xreal_0(k4_power(c3_2__ali2,c2_2_1_1_1_2__ali2),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2,dt_c1_2__ali2,dt_c2_2__ali2,e1_2_1_1_1_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k3_power,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k4_power,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_power,dt_k5_numbers,dt_m2_subset_1,dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2,dt_c3_2__ali2,fc2_membered,e7_2_1_1_1__ali2,e1_2_1_1_1_2__ali2]),
    [interesting(0.2),file(ali2,e3_2_1_1_1_2__ali2),[file(ali2,e3_2_1_1_1_2__ali2)]]).

fof(e2_2_1_1_1_2__ali2,plain,(
    r1_xreal_0(0,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k8_funct_2,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,t5_metric_1]),
    [interesting(0.2),file(ali2,e2_2_1_1_1_2__ali2),[file(ali2,e2_2_1_1_1_2__ali2)]]).

fof(t66_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(0,C) )
               => r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t66_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t66_xreal_1)]).

fof(e4_2_1_1_1_2__ali2,plain,(
    r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_1_1_2__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2,e1_2_1_1_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_1_2__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_2_1_1_1_2__ali2,e2_2_1_1_1_2__ali2,t66_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.2),file(ali2,e4_2_1_1_1_2__ali2),[file(ali2,e4_2_1_1_1_2__ali2)]]).

fof(i3_2_1_1_1_2__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i3_2_1_1_1_2__ali2)]),
    [interesting(0.2),trivial,file(ali2,i3_2_1_1_1_2__ali2)]).

fof(i2_2_1_1_1_2__ali2,plain,(
    r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_1_1_2__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2,e1_2_1_1_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e4_2_1_1_1_2__ali2,i3_2_1_1_1_2__ali2]),
    [interesting(0.2),file(ali2,i2_2_1_1_1_2__ali2),[file(ali2,i2_2_1_1_1_2__ali2)]]).

fof(i1_2_1_1_1_2__ali2,plain,
    ( r1_xreal_0(c1_2_1_1_1_2__ali2,c2_2_1_1_1_2__ali2)
   => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_1_1_2__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e1_2_1_1_1_2__ali2])],[e1_2_1_1_1_2__ali2,i2_2_1_1_1_2__ali2]),
    [interesting(0.2),file(ali2,i1_2_1_1_1_2__ali2),[file(ali2,i1_2_1_1_1_2__ali2)]]).

fof(i1_2_1_1_1_2_tmp__ali2,plain,
    ( ( m2_subset_1(c1_2_1_1_1_2__ali2,k1_numbers,k5_numbers)
      & m2_subset_1(c2_2_1_1_1_2__ali2,k1_numbers,k5_numbers) )
   => ( r1_xreal_0(c1_2_1_1_1_2__ali2,c2_2_1_1_1_2__ali2)
     => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c2_2_1_1_1_2__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_1_2__ali2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2])],[dt_c1_2_1_1_1_2__ali2,dt_c2_2_1_1_1_2__ali2,i1_2_1_1_1_2__ali2]),
    [interesting(0.35),e8_2_1_1_1__ali2]).

fof(e8_2_1_1_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,B)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,A))) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[i1_2_1_1_1_2_tmp__ali2,dh_c1_2_1_1_1_2__ali2,dh_c2_2_1_1_1_2__ali2]),
    [interesting(0.35),file(ali2,e8_2_1_1_1__ali2),[file(ali2,e8_2_1_1_1__ali2)]]).

fof(e5_2_1_1_1_3_1_1_1__ali2,plain,(
    r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e1_2_1_1_1_3_1_1__ali2])],[dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc6_membered,rc1_membered,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,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2__ali2,dt_c4_2_1_1_1__ali2,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e8_2_1_1_1__ali2,e1_2_1_1_1_3_1_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e5_2_1_1_1_3_1_1_1__ali2),[file(ali2,e5_2_1_1_1_3_1_1_1__ali2)]]).

fof(e4_2_1_1_1_3_1_1_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c2_2_1_1_1_3_1_1_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c2_2_1_1_1_3_1_1_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2))) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[dh_c2_2_1_1_1_3_1_1_1__ali2,e2_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),file(ali2,e4_2_1_1_1_3_1_1_1__ali2),[file(ali2,e4_2_1_1_1_3_1_1_1__ali2)]]).

fof(e6_2_1_1_1_3_1_1_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c2_2_1_1_1_3_1_1_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c2_2_1_1_1_3_1_1_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1_3_1_1_1__ali2,dt_c3_2__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2__ali2,dt_c4_2_1_1_1__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e5_2_1_1_1_3_1_1_1__ali2,e4_2_1_1_1_3_1_1_1__ali2,t2_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e6_2_1_1_1_3_1_1_1__ali2),[file(ali2,e6_2_1_1_1_3_1_1_1__ali2)]]).

fof(e4_2_1_1_1__ali2,plain,(
    c1_2_1_1_1__ali2 = a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c3_2_1_1_1__ali2) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c3_2_1_1_1__ali2,e3_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,e4_2_1_1_1__ali2),[file(ali2,e4_2_1_1_1__ali2)]]).

fof(e3_2_1_1_1_3_1_1_1__ali2,plain,(
    c1_2_1_1_1_3_1_1_1__ali2 = c2_2_1_1_1_3_1_1_1__ali2 ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[dh_c2_2_1_1_1_3_1_1_1__ali2,e2_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),file(ali2,e3_2_1_1_1_3_1_1_1__ali2),[file(ali2,e3_2_1_1_1_3_1_1_1__ali2)]]).

fof(e7_2_1_1_1_3_1_1_1__ali2,plain,(
    r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c1_2_1_1_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_1__ali2,dt_c1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1_3_1_1_1__ali2,dt_c3_2__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e6_2_1_1_1_3_1_1_1__ali2,e4_2_1_1_1__ali2,e3_2_1_1_1_3_1_1_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e7_2_1_1_1_3_1_1_1__ali2),[file(ali2,e7_2_1_1_1_3_1_1_1__ali2)]]).

fof(i3_2_1_1_1_3_1_1_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i3_2_1_1_1_3_1_1_1__ali2)]),
    [interesting(0.02),trivial,file(ali2,i3_2_1_1_1_3_1_1_1__ali2)]).

fof(i2_2_1_1_1_3_1_1_1__ali2,plain,(
    r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c1_2_1_1_1__ali2) ),
    inference(conclusion,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c1_2_1_1_1_3_1_1_1__ali2,e1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[e7_2_1_1_1_3_1_1_1__ali2,i3_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),file(ali2,i2_2_1_1_1_3_1_1_1__ali2),[file(ali2,i2_2_1_1_1_3_1_1_1__ali2)]]).

fof(i1_2_1_1_1_3_1_1_1__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c2_2_1_1_1__ali2)
      & ~ r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c1_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c1_2_1_1_1_3_1_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2]),discharge_asm(discharge,[e1_2_1_1_1_3_1_1_1__ali2])],[e1_2_1_1_1_3_1_1_1__ali2,i2_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),file(ali2,i1_2_1_1_1_3_1_1_1__ali2),[file(ali2,i1_2_1_1_1_3_1_1_1__ali2)]]).

fof(i1_2_1_1_1_3_1_1_1_tmp__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c2_2_1_1_1__ali2)
      & ~ r2_hidden(c1_2_1_1_1_3_1_1_1__ali2,c1_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2]),discharge_asm(discharge,[dt_c1_2_1_1_1_3_1_1_1__ali2])],[dt_c1_2_1_1_1_3_1_1_1__ali2,i1_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),e2_2_1_1_1_3_1_1__ali2]).

fof(e2_2_1_1_1_3_1_1__ali2,plain,(
    r1_tarski(c2_2_1_1_1__ali2,c1_2_1_1_1__ali2) ),
    inference(let,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[i1_2_1_1_1_3_1_1_1_tmp__ali2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,d3_tarski,dh_c1_2_1_1_1_3_1_1_1__ali2]),
    [interesting(0.02),file(ali2,e2_2_1_1_1_3_1_1__ali2),[file(ali2,e2_2_1_1_1_3_1_1__ali2)]]).

fof(i2_2_1_1_1_3_1_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i2_2_1_1_1_3_1_1__ali2)]),
    [interesting(0.02),trivial,file(ali2,i2_2_1_1_1_3_1_1__ali2)]).

fof(i1_2_1_1_1_3_1_1__ali2,plain,(
    r1_tarski(c2_2_1_1_1__ali2,c1_2_1_1_1__ali2) ),
    inference(conclusion,[status(thm),assumptions([e1_2_1_1_1_3_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[e2_2_1_1_1_3_1_1__ali2,i2_2_1_1_1_3_1_1__ali2]),
    [interesting(0.02),file(ali2,i1_2_1_1_1_3_1_1__ali2),[file(ali2,i1_2_1_1_1_3_1_1__ali2)]]).

fof(i1_2_1_1_1_3_1__ali2,plain,
    ( r1_xreal_0(c3_2_1_1_1__ali2,c4_2_1_1_1__ali2)
   => ( r1_xreal_0(c3_2_1_1_1__ali2,c4_2_1_1_1__ali2)
      & r1_tarski(c2_2_1_1_1__ali2,c1_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2]),discharge_asm(discharge,[e1_2_1_1_1_3_1_1__ali2])],[e1_2_1_1_1_3_1_1__ali2,i1_2_1_1_1_3_1_1__ali2]),
    [interesting(0.05),file(ali2,i1_2_1_1_1_3_1__ali2),[file(ali2,i1_2_1_1_1_3_1__ali2)]]).

fof(e1_2_1_1_1_3_1_2__ali2,assumption,(
    r1_xreal_0(c4_2_1_1_1__ali2,c3_2_1_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_3_1_2__ali2)]),
    [interesting(0.02),axiom,file(ali2,e1_2_1_1_1_3_1_2__ali2)]).

fof(dt_c1_2_1_1_1_3_1_2_1__ali2,assumption,(
    $true ),
    introduced(assumption,[file(ali2,c1_2_1_1_1_3_1_2_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,c1_2_1_1_1_3_1_2_1__ali2)]).

fof(dh_c1_2_1_1_1_3_1_2_1__ali2,definition,
    ( ~ ( r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c1_2_1_1_1__ali2)
        & ~ r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c2_2_1_1_1__ali2) )
   => ! [A] : 
        ~ ( r2_hidden(A,c1_2_1_1_1__ali2)
          & ~ r2_hidden(A,c2_2_1_1_1__ali2) ) ),
    introduced(definition,[new_symbol(c1_2_1_1_1_3_1_2_1__ali2),file(ali2,c1_2_1_1_1_3_1_2_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,c1_2_1_1_1_3_1_2_1__ali2)]).

fof(e1_2_1_1_1_3_1_2_1__ali2,assumption,(
    r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c1_2_1_1_1__ali2) ),
    introduced(assumption,[file(ali2,e1_2_1_1_1_3_1_2_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,e1_2_1_1_1_3_1_2_1__ali2)]).

fof(dh_c2_2_1_1_1_3_1_2_1__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
        & c1_2_1_1_1_3_1_2_1__ali2 = A
        & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2))) )
   => ( m1_subset_1(c2_2_1_1_1_3_1_2_1__ali2,u1_struct_0(c1_2__ali2))
      & c1_2_1_1_1_3_1_2_1__ali2 = c2_2_1_1_1_3_1_2_1__ali2
      & r1_xreal_0(k4_metric_1(c1_2__ali2,c2_2_1_1_1_3_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c2_2_1_1_1_3_1_2_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2))) ) ),
    introduced(definition,[new_symbol(c2_2_1_1_1_3_1_2_1__ali2),file(ali2,c2_2_1_1_1_3_1_2_1__ali2)]),
    [interesting(0.02),axiom,file(ali2,c2_2_1_1_1_3_1_2_1__ali2)]).

fof(e2_2_1_1_1_3_1_2_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & c1_2_1_1_1_3_1_2_1__ali2 = A
      & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_1__ali2,dt_c1_2_1_1_1_3_1_2_1__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e1_2_1_1_1_3_1_2_1__ali2,e4_2_1_1_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e2_2_1_1_1_3_1_2_1__ali2),[file(ali2,e2_2_1_1_1_3_1_2_1__ali2)]]).

fof(dt_c2_2_1_1_1_3_1_2_1__ali2,plain,(
    m1_subset_1(c2_2_1_1_1_3_1_2_1__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1_1_1_3_1_2_1__ali2,e2_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),file(ali2,c2_2_1_1_1_3_1_2_1__ali2),[file(ali2,c2_2_1_1_1_3_1_2_1__ali2)]]).

fof(e5_2_1_1_1_3_1_2_1__ali2,plain,(
    r1_xreal_0(k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e1_2_1_1_1_3_1_2__ali2])],[dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc6_membered,rc1_membered,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,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2__ali2,dt_c4_2_1_1_1__ali2,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e8_2_1_1_1__ali2,e1_2_1_1_1_3_1_2__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e5_2_1_1_1_3_1_2_1__ali2),[file(ali2,e5_2_1_1_1_3_1_2_1__ali2)]]).

fof(e4_2_1_1_1_3_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c2_2_1_1_1_3_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c2_2_1_1_1_3_1_2_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c3_2_1_1_1__ali2))) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1_1_1_3_1_2_1__ali2,e2_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),file(ali2,e4_2_1_1_1_3_1_2_1__ali2),[file(ali2,e4_2_1_1_1_3_1_2_1__ali2)]]).

fof(e6_2_1_1_1_3_1_2_1__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c2_2_1_1_1_3_1_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c2_2_1_1_1_3_1_2_1__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c4_2_1_1_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1_3_1_2_1__ali2,dt_c3_2__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2__ali2,dt_c4_2_1_1_1__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e5_2_1_1_1_3_1_2_1__ali2,e4_2_1_1_1_3_1_2_1__ali2,t2_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e6_2_1_1_1_3_1_2_1__ali2),[file(ali2,e6_2_1_1_1_3_1_2_1__ali2)]]).

fof(e3_2_1_1_1_3_1_2_1__ali2,plain,(
    c1_2_1_1_1_3_1_2_1__ali2 = c2_2_1_1_1_3_1_2_1__ali2 ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1_1_1_3_1_2_1__ali2,e2_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),file(ali2,e3_2_1_1_1_3_1_2_1__ali2),[file(ali2,e3_2_1_1_1_3_1_2_1__ali2)]]).

fof(e7_2_1_1_1_3_1_2_1__ali2,plain,(
    r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c2_2_1_1_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_1_3_1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_1_1__ali2,dt_c2_2_1_1_1_3_1_2_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,dt_c4_2_1_1_1__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e6_2_1_1_1_3_1_2_1__ali2,e6_2_1_1_1__ali2,e3_2_1_1_1_3_1_2_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.02),file(ali2,e7_2_1_1_1_3_1_2_1__ali2),[file(ali2,e7_2_1_1_1_3_1_2_1__ali2)]]).

fof(i3_2_1_1_1_3_1_2_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i3_2_1_1_1_3_1_2_1__ali2)]),
    [interesting(0.02),trivial,file(ali2,i3_2_1_1_1_3_1_2_1__ali2)]).

fof(i2_2_1_1_1_3_1_2_1__ali2,plain,(
    r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c2_2_1_1_1__ali2) ),
    inference(conclusion,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1_1_3_1_2_1__ali2,e1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e7_2_1_1_1_3_1_2_1__ali2,i3_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),file(ali2,i2_2_1_1_1_3_1_2_1__ali2),[file(ali2,i2_2_1_1_1_3_1_2_1__ali2)]]).

fof(i1_2_1_1_1_3_1_2_1__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c1_2_1_1_1__ali2)
      & ~ r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c2_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1_1_3_1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e1_2_1_1_1_3_1_2_1__ali2])],[e1_2_1_1_1_3_1_2_1__ali2,i2_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),file(ali2,i1_2_1_1_1_3_1_2_1__ali2),[file(ali2,i1_2_1_1_1_3_1_2_1__ali2)]]).

fof(i1_2_1_1_1_3_1_2_1_tmp__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c1_2_1_1_1__ali2)
      & ~ r2_hidden(c1_2_1_1_1_3_1_2_1__ali2,c2_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_1_1_3_1_2_1__ali2])],[dt_c1_2_1_1_1_3_1_2_1__ali2,i1_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),e2_2_1_1_1_3_1_2__ali2]).

fof(e2_2_1_1_1_3_1_2__ali2,plain,(
    r1_tarski(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ),
    inference(let,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[i1_2_1_1_1_3_1_2_1_tmp__ali2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,d3_tarski,dh_c1_2_1_1_1_3_1_2_1__ali2]),
    [interesting(0.02),file(ali2,e2_2_1_1_1_3_1_2__ali2),[file(ali2,e2_2_1_1_1_3_1_2__ali2)]]).

fof(i2_2_1_1_1_3_1_2__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i2_2_1_1_1_3_1_2__ali2)]),
    [interesting(0.02),trivial,file(ali2,i2_2_1_1_1_3_1_2__ali2)]).

fof(i1_2_1_1_1_3_1_2__ali2,plain,(
    r1_tarski(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ),
    inference(conclusion,[status(thm),assumptions([e1_2_1_1_1_3_1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e2_2_1_1_1_3_1_2__ali2,i2_2_1_1_1_3_1_2__ali2]),
    [interesting(0.02),file(ali2,i1_2_1_1_1_3_1_2__ali2),[file(ali2,i1_2_1_1_1_3_1_2__ali2)]]).

fof(i2_2_1_1_1_3_1__ali2,plain,
    ( r1_xreal_0(c4_2_1_1_1__ali2,c3_2_1_1_1__ali2)
   => ( r1_xreal_0(c4_2_1_1_1__ali2,c3_2_1_1_1__ali2)
      & r1_tarski(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e1_2_1_1_1_3_1_2__ali2])],[e1_2_1_1_1_3_1_2__ali2,i1_2_1_1_1_3_1_2__ali2]),
    [interesting(0.05),file(ali2,i2_2_1_1_1_3_1__ali2),[file(ali2,i2_2_1_1_1_3_1__ali2)]]).

fof(e1_2_1_1_1_3_1__ali2,plain,
    ( r1_xreal_0(c3_2_1_1_1__ali2,c4_2_1_1_1__ali2)
    | r1_xreal_0(c4_2_1_1_1__ali2,c3_2_1_1_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_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,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_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_numbers,dt_m2_subset_1,cc2_xreal_0,fc2_membered,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c3_2_1_1_1__ali2,dt_c4_2_1_1_1__ali2]),
    [interesting(0.05),file(ali2,e1_2_1_1_1_3_1__ali2),[file(ali2,e1_2_1_1_1_3_1__ali2)]]).

fof(e9_2_1_1_1__ali2,plain,
    ( ( r1_xreal_0(c3_2_1_1_1__ali2,c4_2_1_1_1__ali2)
      & r1_tarski(c2_2_1_1_1__ali2,c1_2_1_1_1__ali2) )
    | ( r1_xreal_0(c4_2_1_1_1__ali2,c3_2_1_1_1__ali2)
      & r1_tarski(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ) ),
    inference(percases,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[i1_2_1_1_1_3_1__ali2,i2_2_1_1_1_3_1__ali2,e1_2_1_1_1_3_1__ali2]),
    [interesting(0.35),file(ali2,e9_2_1_1_1__ali2),[file(ali2,e9_2_1_1_1__ali2)]]).

fof(e10_2_1_1_1__ali2,plain,
    ( r1_tarski(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2)
    | r1_tarski(c2_2_1_1_1__ali2,c1_2_1_1_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc7_xreal_0,fc1_ordinal2,fc5_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,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,cc2_xreal_0,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,dt_c3_2_1_1_1__ali2,dt_c4_2_1_1_1__ali2,t3_subset,e9_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,e10_2_1_1_1__ali2),[file(ali2,e10_2_1_1_1__ali2)]]).

fof(i3_2_1_1_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i3_2_1_1_1__ali2)]),
    [interesting(0.35),trivial,file(ali2,i3_2_1_1_1__ali2)]).

fof(i2_2_1_1_1__ali2,plain,(
    r3_xboole_0(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e1_2_1_1_1__ali2,e3_2_1_1__ali2])],[reflexivity_r1_tarski,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,d9_xboole_0,e10_2_1_1_1__ali2,i3_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,i2_2_1_1_1__ali2),[file(ali2,i2_2_1_1_1__ali2)]]).

fof(i1_2_1_1_1__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1_1__ali2)
      & r2_hidden(c2_2_1_1_1__ali2,c1_2_1_1__ali2)
      & ~ r3_xboole_0(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,e3_2_1_1__ali2]),discharge_asm(discharge,[e1_2_1_1_1__ali2])],[e1_2_1_1_1__ali2,i2_2_1_1_1__ali2]),
    [interesting(0.35),file(ali2,i1_2_1_1_1__ali2),[file(ali2,i1_2_1_1_1__ali2)]]).

fof(i1_2_1_1_1_tmp__ali2,plain,(
    ~ ( r2_hidden(c1_2_1_1_1__ali2,c1_2_1_1__ali2)
      & r2_hidden(c2_2_1_1_1__ali2,c1_2_1_1__ali2)
      & ~ r3_xboole_0(c1_2_1_1_1__ali2,c2_2_1_1_1__ali2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2]),discharge_asm(discharge,[dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2])],[dt_c1_2_1_1_1__ali2,dt_c2_2_1_1_1__ali2,i1_2_1_1_1__ali2]),
    [interesting(0.5),e5_2_1_1__ali2]).

fof(e5_2_1_1__ali2,plain,(
    v6_ordinal1(c1_2_1_1__ali2) ),
    inference(let,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2])],[i1_2_1_1_1_tmp__ali2,antisymmetry_r2_hidden,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_c1_2_1_1__ali2,d9_ordinal1,dh_c1_2_1_1_1__ali2,dh_c2_2_1_1_1__ali2]),
    [interesting(0.5),file(ali2,e5_2_1_1__ali2),[file(ali2,e5_2_1_1__ali2)]]).

fof(t30_finset_1,theorem,(
    ! [A] : 
      ~ ( v1_finset_1(A)
        & A != k1_xboole_0
        & v6_ordinal1(A)
        & ! [B] : 
            ~ ( r2_hidden(B,A)
              & ! [C] : 
                  ( r2_hidden(C,A)
                 => r1_tarski(B,C) ) ) ) ),
    file(finset_1,t30_finset_1),
    [interesting(0.9),axiom,file(finset_1,t30_finset_1)]).

fof(e6_2_1_1__ali2,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_2_1_1__ali2)
      & ! [B] : 
          ( r2_hidden(B,c1_2_1_1__ali2)
         => r1_tarski(A,B) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_2_1_1__ali2,fc6_membered,t1_subset,t3_subset,t6_boole,t7_boole,e5_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2,t30_finset_1]),
    [interesting(0.5),file(ali2,e6_2_1_1__ali2),[file(ali2,e6_2_1_1__ali2)]]).

fof(dt_c2_2_1_1__ali2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[dh_c2_2_1_1__ali2,e6_2_1_1__ali2]),
    [interesting(0.5),file(ali2,c2_2_1_1__ali2),[file(ali2,c2_2_1_1__ali2)]]).

fof(fraenkel_a_4_1_ali2,definition,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(B)
        & v6_metric_1(B)
        & v7_metric_1(B)
        & v8_metric_1(B)
        & v9_metric_1(B)
        & l1_metric_1(B)
        & m1_ali2(C,B)
        & m1_subset_1(D,k1_numbers)
        & m1_subset_1(E,u1_struct_0(B)) )
     => ( r2_hidden(A,a_4_1_ali2(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,u1_struct_0(B))
            & A = F
            & r1_xreal_0(k4_metric_1(B,F,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,F)),k4_real_1(k4_metric_1(B,E,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E)),k4_power(D,0))) ) ) ) ),
    file(ali2,a_4_1_ali2),
    [interesting(0.9),axiom,file(ali2,a_4_1_ali2)]).

fof(fraenkel_a_5_1_ali2,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(B)
        & v6_metric_1(B)
        & v7_metric_1(B)
        & v8_metric_1(B)
        & v9_metric_1(B)
        & l1_metric_1(B)
        & m1_ali2(C,B)
        & m1_subset_1(D,k1_numbers)
        & m1_subset_1(E,u1_struct_0(B))
        & m2_subset_1(F,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_5_1_ali2(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,u1_struct_0(B))
            & A = G
            & r1_xreal_0(k4_metric_1(B,G,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,G)),k4_real_1(k4_metric_1(B,E,k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E)),k4_power(D,k1_nat_1(F,1)))) ) ) ) ),
    file(ali2,a_5_1_ali2),
    [interesting(0.9),axiom,file(ali2,a_5_1_ali2)]).

fof(s1_nat_1__e15_2_1_1__ali2,theorem,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A)
        & m1_ali2(B,A)
        & m1_subset_1(C,k1_numbers)
        & m1_subset_1(D,u1_struct_0(A)) )
     => ( ( a_4_1_ali2(A,B,C,D) != k1_xboole_0
          & ! [E] : 
              ( m2_subset_1(E,k1_numbers,k5_numbers)
             => ( a_5_0_ali2(A,B,C,D,E) != k1_xboole_0
               => a_5_1_ali2(A,B,C,D,E) != k1_xboole_0 ) ) )
       => ! [E] : 
            ( m2_subset_1(E,k1_numbers,k5_numbers)
           => a_5_0_ali2(A,B,C,D,E) != k1_xboole_0 ) ) ) ),
    file(ali2,s1_nat_1__e15_2_1_1__ali2),
    [interesting(0.9),axiom,file(ali2,s1_nat_1__e15_2_1_1__ali2)]).

fof(e1_2_1_1_2__ali2,plain,(
    k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc4_subset_1,fc4_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,spc1_numerals,spc1_boole,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e1_2_1_1_2__ali2),[file(ali2,e1_2_1_1_2__ali2)]]).

fof(t29_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k3_power(A,0) = 1 ) ),
    file(power,t29_power),
    [interesting(0.9),axiom,file(power,t29_power)]).

fof(e2_2_1_1_2__ali2,plain,(
    k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),1) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_power,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc2_xreal_0,fc4_xreal_0,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,t29_power,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e2_2_1_1_2__ali2),[file(ali2,e2_2_1_1_2__ali2)]]).

fof(e11_2_1_1__ali2,plain,(
    k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,0)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[e1_2_1_1_2__ali2,e2_2_1_1_2__ali2]),
    [interesting(0.5),file(ali2,e11_2_1_1__ali2),[file(ali2,e11_2_1_1__ali2)]]).

fof(e12_2_1_1__ali2,plain,(
    r2_hidden(c4_2__ali2,a_4_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_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,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc30_xreal_0,fc4_xreal_0,fc5_membered,fc5_xreal_0,fc6_membered,fc6_xreal_0,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,t1_real,t3_subset,t4_real,t4_subset,t5_subset,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,antisymmetry_r2_hidden,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,t1_subset,t7_boole,t2_tarski,fraenkel_a_4_1_ali2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e11_2_1_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0]),
    [interesting(0.5),file(ali2,e12_2_1_1__ali2),[file(ali2,e12_2_1_1__ali2)]]).

fof(e13_2_1_1__ali2,plain,(
    a_4_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_real,t3_subset,t4_real,t4_subset,t5_subset,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_ali2,existence_m1_subset_1,existence_m2_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_membered,rc1_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_boole,spc0_numerals,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t8_boole,spc0_numerals,spc0_boole,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_xcmplx_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,fc6_membered,t1_subset,t6_boole,t7_boole,t2_tarski,fraenkel_a_4_1_ali2,spc1_numerals,spc1_boole,e12_2_1_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ali2,e13_2_1_1__ali2),[file(ali2,e13_2_1_1__ali2)]]).

fof(dh_c1_2_1_1_3__ali2,definition,
    ( ( m2_subset_1(c1_2_1_1_3__ali2,k1_numbers,k5_numbers)
     => ( a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0
       => a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0 ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) != k1_xboole_0
         => a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) != k1_xboole_0 ) ) ),
    introduced(definition,[new_symbol(c1_2_1_1_3__ali2),file(ali2,c1_2_1_1_3__ali2)]),
    [interesting(0.35),axiom,file(ali2,c1_2_1_1_3__ali2)]).

fof(e2_2_1_1_3__ali2,assumption,(
    a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0 ),
    introduced(assumption,[file(ali2,e2_2_1_1_3__ali2)]),
    [interesting(0.35),axiom,file(ali2,e2_2_1_1_3__ali2)]).

fof(dt_c1_2_1_1_3__ali2,assumption,(
    m2_subset_1(c1_2_1_1_3__ali2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(ali2,c1_2_1_1_3__ali2)]),
    [interesting(0.35),axiom,file(ali2,c1_2_1_1_3__ali2)]).

fof(dh_c3_2_1_1_3__ali2,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
        & A = c2_2_1_1_3__ali2
        & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) )
   => ( m1_subset_1(c3_2_1_1_3__ali2,u1_struct_0(c1_2__ali2))
      & c3_2_1_1_3__ali2 = c2_2_1_1_3__ali2
      & r1_xreal_0(k4_metric_1(c1_2__ali2,c3_2_1_1_3__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) ) ),
    introduced(definition,[new_symbol(c3_2_1_1_3__ali2),file(ali2,c3_2_1_1_3__ali2)]),
    [interesting(0.35),axiom,file(ali2,c3_2_1_1_3__ali2)]).

fof(dh_c2_2_1_1_3__ali2,definition,
    ( ? [A] : m1_subset_1(A,a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2))
   => m1_subset_1(c2_2_1_1_3__ali2,a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2)) ),
    introduced(definition,[new_symbol(c2_2_1_1_3__ali2),file(ali2,c2_2_1_1_3__ali2)]),
    [interesting(0.35),axiom,file(ali2,c2_2_1_1_3__ali2)]).

fof(e1_2_1_1_3__ali2,plain,(
    ? [A] : m1_subset_1(A,a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_real,t3_subset,t4_real,t4_subset,t5_subset,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_l1_metric_1,existence_m1_ali2,existence_m2_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_metric_1,dt_m1_ali2,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r1,spc7_arithm,t1_subset,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,existence_m1_subset_1,dt_k3_xcmplx_0,dt_m1_subset_1,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e1_2_1_1_3__ali2),[file(ali2,e1_2_1_1_3__ali2)]]).

fof(dt_c2_2_1_1_3__ali2,plain,(
    m1_subset_1(c2_2_1_1_3__ali2,a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1_1_3__ali2,e1_2_1_1_3__ali2]),
    [interesting(0.35),file(ali2,c2_2_1_1_3__ali2),[file(ali2,c2_2_1_1_3__ali2)]]).

fof(e3_2_1_1_3__ali2,plain,(
    r2_hidden(c2_2_1_1_3__ali2,a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e2_2_1_1_3__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k3_power,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_real,t3_subset,t4_real,t4_subset,t5_subset,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_ali2,existence_m1_subset_1,existence_m2_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_membered,rc1_membered,rqLessOrEqual__r1_xreal_0__r1_r1,spc7_arithm,t2_subset,t3_arithm,t8_boole,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_xcmplx_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c2_2_1_1_3__ali2,dt_c3_2__ali2,dt_c4_2__ali2,fc6_membered,t1_subset,t6_boole,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e2_2_1_1_3__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e3_2_1_1_3__ali2),[file(ali2,e3_2_1_1_3__ali2)]]).

fof(e4_2_1_1_3__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & A = c2_2_1_1_3__ali2
      & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e2_2_1_1_3__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c2_2_1_1_3__ali2,dt_c3_2__ali2,dt_c4_2__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,spc1_numerals,spc1_boole,e3_2_1_1_3__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e4_2_1_1_3__ali2),[file(ali2,e4_2_1_1_3__ali2)]]).

fof(dt_c3_2_1_1_3__ali2,plain,(
    m1_subset_1(c3_2_1_1_3__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e2_2_1_1_3__ali2])],[dh_c3_2_1_1_3__ali2,e4_2_1_1_3__ali2]),
    [interesting(0.35),file(ali2,c3_2_1_1_3__ali2),[file(ali2,c3_2_1_1_3__ali2)]]).

fof(e9_2_1_1_3__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2))),k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,c3_2_1_1_3__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,e2_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_3__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e3_2__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e9_2_1_1_3__ali2),[file(ali2,e9_2_1_1_3__ali2)]]).

fof(e6_2_1_1_3__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,c3_2_1_1_3__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) ),
    inference(consider,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e2_2_1_1_3__ali2])],[dh_c3_2_1_1_3__ali2,e4_2_1_1_3__ali2]),
    [interesting(0.35),file(ali2,e6_2_1_1_3__ali2),[file(ali2,e6_2_1_1_3__ali2)]]).

fof(e7_2_1_1_3__ali2,plain,(
    r1_xreal_0(k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,c3_2_1_1_3__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2))),k4_real_1(c3_2__ali2,k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e2_2_1_1_3__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_3__ali2,dt_c4_2__ali2,cc2_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_2__ali2,e6_2_1_1_3__ali2,t66_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.35),file(ali2,e7_2_1_1_3__ali2),[file(ali2,e7_2_1_1_3__ali2)]]).

fof(e1_2_1_1_3_1__ali2,plain,(
    k4_real_1(c3_2__ali2,k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_real_1(c3_2__ali2,k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc4_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,spc1_numerals,spc1_boole,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.2),file(ali2,e1_2_1_1_3_1__ali2),[file(ali2,e1_2_1_1_3_1__ali2)]]).

fof(t30_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k3_power(A,1) = A ) ),
    file(power,t30_power),
    [interesting(0.9),axiom,file(power,t30_power)]).

fof(e2_2_1_1_3_1__ali2,plain,(
    k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_real_1(c3_2__ali2,k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_real_1(k4_power(c3_2__ali2,c1_2_1_1_3__ali2),k4_power(c3_2__ali2,1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,rc3_struct_0,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_power,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc2_xreal_0,fc4_xreal_0,spc1_numerals,spc1_boole,t30_power,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.2),file(ali2,e2_2_1_1_3_1__ali2),[file(ali2,e2_2_1_1_3_1__ali2)]]).

fof(t32_power,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ~ r1_xreal_0(A,0)
               => k3_power(A,k2_xcmplx_0(B,C)) = k3_xcmplx_0(k3_power(A,B),k3_power(A,C)) ) ) ) ) ),
    file(power,t32_power),
    [interesting(0.9),axiom,file(power,t32_power)]).

fof(e3_2_1_1_3_1__ali2,plain,(
    k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_real_1(k4_power(c3_2__ali2,c1_2_1_1_3__ali2),k4_power(c3_2__ali2,1))) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,k1_nat_1(c1_2_1_1_3__ali2,1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k3_power,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc2_xreal_0,fc3_xreal_0,fc4_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,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,e2_2__ali2,t32_power,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.2),file(ali2,e3_2_1_1_3_1__ali2),[file(ali2,e3_2_1_1_3_1__ali2)]]).

fof(e8_2_1_1_3__ali2,plain,(
    k4_real_1(c3_2__ali2,k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,c1_2_1_1_3__ali2))) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,k1_nat_1(c1_2_1_1_3__ali2,1))) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[e1_2_1_1_3_1__ali2,e2_2_1_1_3_1__ali2,e3_2_1_1_3_1__ali2]),
    [interesting(0.35),file(ali2,e8_2_1_1_3__ali2),[file(ali2,e8_2_1_1_3__ali2)]]).

fof(e10_2_1_1_3__ali2,plain,(
    r1_xreal_0(k4_metric_1(c1_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2),k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2))),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,k1_nat_1(c1_2_1_1_3__ali2,1)))) ),
    inference(mizar_by,[status(thm),assumptions([e2_2_1_1_3__ali2,dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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_ordinal2,fc1_subset_1,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc3_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,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,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,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k1_nat_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_3__ali2,dt_c4_2__ali2,cc2_xreal_0,fc1_xreal_0,fc4_xreal_0,fc5_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_2_1_1_3__ali2,e7_2_1_1_3__ali2,e8_2_1_1_3__ali2,t2_xreal_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.35),file(ali2,e10_2_1_1_3__ali2),[file(ali2,e10_2_1_1_3__ali2)]]).

fof(e11_2_1_1_3__ali2,plain,(
    r2_hidden(k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1_1_3__ali2),a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([e2_2_1_1_3__ali2,dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k1_nat_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k1_nat_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_3__ali2,dt_c4_2__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_1_ali2,spc1_numerals,spc1_boole,e10_2_1_1_3__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e11_2_1_1_3__ali2),[file(ali2,e11_2_1_1_3__ali2)]]).

fof(e12_2_1_1_3__ali2,plain,(
    a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e2_2_1_1_3__ali2,dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,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,fc4_subset_1,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_ordinal2,dt_m2_relset_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_membered,fc8_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,spc5_arithm,spc6_arithm,t1_real,t3_subset,t4_real,t4_subset,t5_subset,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc2_membered,rc1_membered,rc3_struct_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc7_arithm,t2_subset,t3_arithm,t8_boole,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,redefinition_k8_funct_2,dt_k1_xboole_0,dt_k3_xcmplx_0,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_1_3__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1_1_3__ali2,dt_c4_2__ali2,fc6_membered,t1_subset,t6_boole,t7_boole,t2_tarski,fraenkel_a_5_1_ali2,spc1_numerals,spc1_boole,e11_2_1_1_3__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e12_2_1_1_3__ali2),[file(ali2,e12_2_1_1_3__ali2)]]).

fof(i3_2_1_1_3__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i3_2_1_1_3__ali2)]),
    [interesting(0.35),trivial,file(ali2,i3_2_1_1_3__ali2)]).

fof(i2_2_1_1_3__ali2,plain,(
    a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([e2_2_1_1_3__ali2,dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[e12_2_1_1_3__ali2,i3_2_1_1_3__ali2]),
    [interesting(0.35),file(ali2,i2_2_1_1_3__ali2),[file(ali2,i2_2_1_1_3__ali2)]]).

fof(i1_2_1_1_3__ali2,plain,
    ( a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0
   => a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1_3__ali2,dt_c1_2__ali2,dt_c2_2__ali2]),discharge_asm(discharge,[e2_2_1_1_3__ali2])],[e2_2_1_1_3__ali2,i2_2_1_1_3__ali2]),
    [interesting(0.35),file(ali2,i1_2_1_1_3__ali2),[file(ali2,i1_2_1_1_3__ali2)]]).

fof(i1_2_1_1_3_tmp__ali2,plain,
    ( m2_subset_1(c1_2_1_1_3__ali2,k1_numbers,k5_numbers)
   => ( a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0
     => a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_1_3__ali2) != k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_1_3__ali2])],[dt_c1_2_1_1_3__ali2,i1_2_1_1_3__ali2]),
    [interesting(0.5),e14_2_1_1__ali2]).

fof(e14_2_1_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) != k1_xboole_0
       => a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) != k1_xboole_0 ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[i1_2_1_1_3_tmp__ali2,dh_c1_2_1_1_3__ali2]),
    [interesting(0.5),file(ali2,e14_2_1_1__ali2),[file(ali2,e14_2_1_1__ali2)]]).

fof(e15_2_1_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => a_5_0_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,A) != k1_xboole_0 ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[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,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,dt_k1_funct_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_subset_1,fc4_xreal_0,fc8_xreal_0,rc1_xreal_0,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_nat_1,dt_k1_zfmisc_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_struct_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k5_numbers,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,fc2_membered,fc6_membered,t2_tarski,fraenkel_a_4_1_ali2,fraenkel_a_5_0_ali2,fraenkel_a_5_1_ali2,s1_nat_1__e15_2_1_1__ali2,e13_2_1_1__ali2,e14_2_1_1__ali2]),
    [interesting(0.5),file(ali2,e15_2_1_1__ali2),[file(ali2,e15_2_1_1__ali2)]]).

fof(e7_2_1_1__ali2,plain,(
    r2_hidden(c2_2_1_1__ali2,c1_2_1_1__ali2) ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[dh_c2_2_1_1__ali2,e6_2_1_1__ali2]),
    [interesting(0.5),file(ali2,e7_2_1_1__ali2),[file(ali2,e7_2_1_1__ali2)]]).

fof(e10_2_1_1__ali2,plain,(
    r2_hidden(c2_2_1_1__ali2,c1_2_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,abstractness_v1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_xboole_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc6_membered,rc1_membered,rc3_struct_0,rc5_struct_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,cc15_membered,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_c1_2_1__ali2,dt_c1_2_1_1__ali2,dt_c2_2_1_1__ali2,t1_subset,t3_subset,t7_boole,e3_2_1_1__ali2,e7_2_1_1__ali2]),
    [interesting(0.5),file(ali2,e10_2_1_1__ali2),[file(ali2,e10_2_1_1__ali2)]]).

fof(e16_2_1_1__ali2,plain,(
    c2_2_1_1__ali2 != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc4_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,commutativity_k3_xcmplx_0,abstractness_v1_pre_topc,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc4_xreal_0,rc1_xreal_0,spc7_arithm,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_numbers,dt_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c2_2__ali2,dt_c2_2_1_1__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,fc6_membered,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,e15_2_1_1__ali2,e3_2_1__ali2,e10_2_1_1__ali2]),
    [interesting(0.5),file(ali2,e16_2_1_1__ali2),[file(ali2,e16_2_1_1__ali2)]]).

fof(e8_2_1_1__ali2,plain,(
    ! [A] : 
      ( r2_hidden(A,c1_2_1_1__ali2)
     => r1_tarski(c2_2_1_1__ali2,A) ) ),
    inference(consider,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[dh_c2_2_1_1__ali2,e6_2_1_1__ali2]),
    [interesting(0.5),file(ali2,e8_2_1_1__ali2),[file(ali2,e8_2_1_1__ali2)]]).

fof(t6_setfam_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    file(setfam_1,t6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,t6_setfam_1)]).

fof(e9_2_1_1__ali2,plain,(
    r1_tarski(c2_2_1_1__ali2,k1_setfam_1(c1_2_1_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_setfam_1,dt_k1_xboole_0,dt_c1_2_1_1__ali2,dt_c2_2_1_1__ali2,fc6_membered,t1_subset,t3_subset,t6_boole,t7_boole,e2_2_1_1__ali2,e8_2_1_1__ali2,t6_setfam_1]),
    [interesting(0.5),file(ali2,e9_2_1_1__ali2),[file(ali2,e9_2_1_1__ali2)]]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]).

fof(e17_2_1_1__ali2,plain,(
    k1_setfam_1(c1_2_1_1__ali2) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_setfam_1,dt_k1_xboole_0,dt_c1_2_1_1__ali2,dt_c2_2_1_1__ali2,fc6_membered,t3_subset,t6_boole,e16_2_1_1__ali2,e9_2_1_1__ali2,t3_xboole_1]),
    [interesting(0.5),file(ali2,e17_2_1_1__ali2),[file(ali2,e17_2_1_1__ali2)]]).

fof(i4_2_1_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i4_2_1_1__ali2)]),
    [interesting(0.5),trivial,file(ali2,i4_2_1_1__ali2)]).

fof(i3_2_1_1__ali2,plain,(
    k1_setfam_1(c1_2_1_1__ali2) != k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2,e3_2_1_1__ali2,e2_2_1_1__ali2,e4_2_1_1__ali2])],[e17_2_1_1__ali2,i4_2_1_1__ali2]),
    [interesting(0.5),file(ali2,i3_2_1_1__ali2),[file(ali2,i3_2_1_1__ali2)]]).

fof(i2_2_1_1__ali2,plain,(
    ~ ( c1_2_1_1__ali2 != k1_xboole_0
      & r1_tarski(c1_2_1_1__ali2,c1_2_1__ali2)
      & v1_finset_1(c1_2_1_1__ali2)
      & k1_setfam_1(c1_2_1_1__ali2) = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2,dt_c1_2_1_1__ali2]),discharge_asm(discharge,[e2_2_1_1__ali2,e3_2_1_1__ali2,e4_2_1_1__ali2])],[e2_2_1_1__ali2,e3_2_1_1__ali2,e4_2_1_1__ali2,i3_2_1_1__ali2]),
    [interesting(0.5),file(ali2,i2_2_1_1__ali2),[file(ali2,i2_2_1_1__ali2)]]).

fof(i2_2_1_1_tmp__ali2,plain,(
    ~ ( c1_2_1_1__ali2 != k1_xboole_0
      & r1_tarski(c1_2_1_1__ali2,c1_2_1__ali2)
      & v1_finset_1(c1_2_1_1__ali2)
      & k1_setfam_1(c1_2_1_1__ali2) = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_1__ali2])],[dt_c1_2_1_1__ali2,i2_2_1_1__ali2]),
    [interesting(0.5),i1_2_1_1__ali2]).

fof(i1_2_1_1__ali2,plain,(
    ! [A] : 
      ~ ( A != k1_xboole_0
        & r1_tarski(A,c1_2_1__ali2)
        & v1_finset_1(A)
        & k1_setfam_1(A) = k1_xboole_0 ) ),
    inference(let,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[i2_2_1_1_tmp__ali2,dh_c1_2_1_1__ali2]),
    [interesting(0.5),file(ali2,i1_2_1_1__ali2),[file(ali2,i1_2_1_1__ali2)]]).

fof(e6_2_1__ali2,plain,(
    v1_compts_1(c1_2_1__ali2) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_xreal_0,rc3_struct_0,rc5_struct_0,dt_k1_zfmisc_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,reflexivity_r1_tarski,dt_k1_setfam_1,dt_k1_xboole_0,dt_c1_2_1__ali2,fc6_membered,d2_compts_1,e1_2_1_1__ali2,i1_2_1_1__ali2]),
    [interesting(0.65),file(ali2,e6_2_1__ali2),[file(ali2,e6_2_1__ali2)]]).

fof(t13_compts_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_compts_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
           => ~ ( v1_compts_1(B)
                & v2_tops_2(B,A)
                & k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0 ) ) ) ) ),
    file(compts_1,t13_compts_1),
    [interesting(0.9),axiom,file(compts_1,t13_compts_1)]).

fof(e8_2_1__ali2,plain,(
    k6_setfam_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1__ali2) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,abstractness_v1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_metric_1,existence_l1_struct_0,dt_k1_setfam_1,dt_l1_metric_1,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t7_boole,t8_boole,existence_l1_pre_topc,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_pcomps_1,dt_k6_setfam_1,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,fc1_subset_1,fc6_membered,t3_subset,t6_boole,e7_2_1__ali2,e4_2__ali2,e6_2_1__ali2,t13_compts_1]),
    [interesting(0.65),file(ali2,e8_2_1__ali2),[file(ali2,e8_2_1__ali2)]]).

fof(t10_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ~ ( B != k1_xboole_0
          & ! [C] : 
              ( m1_subset_1(C,A)
             => ~ r2_hidden(C,B) ) ) ) ),
    file(subset_1,t10_subset_1),
    [interesting(0.9),axiom,file(subset_1,t10_subset_1)]).

fof(e9_2_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(k5_pcomps_1(c1_2__ali2)))
      & r2_hidden(A,k6_setfam_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1__ali2)) ) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,abstractness_v1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_setfam_1,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_pcomps_1,dt_k6_setfam_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,fc1_subset_1,fc6_membered,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e8_2_1__ali2,t10_subset_1]),
    [interesting(0.65),file(ali2,e9_2_1__ali2),[file(ali2,e9_2_1__ali2)]]).

fof(dt_c2_2_1__ali2,plain,(
    m1_subset_1(c2_2_1__ali2,u1_struct_0(k5_pcomps_1(c1_2__ali2))) ),
    inference(consider,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1__ali2,e9_2_1__ali2]),
    [interesting(0.65),file(ali2,c2_2_1__ali2),[file(ali2,c2_2_1__ali2)]]).

fof(de_c3_2_1__ali2,definition,(
    c3_2_1__ali2 = c2_2_1__ali2 ),
    introduced(definition,[new_symbol(c3_2_1__ali2),file(ali2,c3_2_1__ali2)]),
    [interesting(0.65),axiom,file(ali2,c3_2_1__ali2)]).

fof(e11_2_1__ali2,plain,(
    m1_subset_1(c2_2_1__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,dt_u1_pre_topc,cc15_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_pre_topc,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_zfmisc_1,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,fc1_struct_0,fc1_subset_1,fc3_pcomps_1,fc4_pcomps_1,rc3_struct_0,t3_subset,free_g1_pre_topc,existence_m1_subset_1,dt_g1_pre_topc,dt_k4_pcomps_1,dt_k5_pcomps_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2_1__ali2,e4_2_1__ali2]),
    [interesting(0.65),file(ali2,e11_2_1__ali2),[file(ali2,e11_2_1__ali2)]]).

fof(dt_c3_2_1__ali2,plain,(
    m1_subset_1(c3_2_1__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[reflexivity_r1_tarski,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k1_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_xreal_0,cc7_xreal_0,fc1_subset_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,free_g1_pre_topc,antisymmetry_r2_hidden,dt_g1_pre_topc,dt_k1_xboole_0,dt_u1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc15_membered,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_metric_1,existence_l1_struct_0,dt_k5_pcomps_1,dt_l1_metric_1,dt_l1_struct_0,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2_1__ali2,de_c3_2_1__ali2,e11_2_1__ali2]),
    [interesting(0.65),file(ali2,c3_2_1__ali2),[file(ali2,c3_2_1__ali2)]]).

fof(cc4_seqm_3,theorem,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v3_seqm_3(A)
          & v4_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v5_seqm_3(A) ) ) ) ),
    file(seqm_3,cc4_seqm_3),
    [interesting(0.9),axiom,file(seqm_3,cc4_seqm_3)]).

fof(fc4_ordinal2,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_ordinal2(k2_funcop_1(A,B)) ) ) ),
    file(ordinal2,fc4_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc4_ordinal2)]).

fof(dt_k12_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_xreal_0(B) )
     => ( v1_relat_1(k12_seq_1(A,B))
        & v1_funct_1(k12_seq_1(A,B)) ) ) ),
    file(seq_1,k12_seq_1),
    [interesting(0.9),axiom,file(seq_1,k12_seq_1)]).

fof(dt_k1_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => v1_xreal_0(k1_seq_2(A)) ) ),
    file(seq_2,k1_seq_2),
    [interesting(0.9),axiom,file(seq_2,k1_seq_2)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(cc3_seqm_3,theorem,(
    ! [A] : 
      ( m1_relset_1(A,k5_numbers,k1_numbers)
     => ( ( v1_funct_1(A)
          & v5_seqm_3(A) )
       => ( v1_funct_1(A)
          & v1_seq_1(A)
          & v3_seqm_3(A)
          & v4_seqm_3(A) ) ) ) ),
    file(seqm_3,cc3_seqm_3),
    [interesting(0.9),axiom,file(seqm_3,cc3_seqm_3)]).

fof(fc2_seqm_3,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B))
      & v5_seqm_3(k2_funcop_1(A,B)) ) ),
    file(seqm_3,fc2_seqm_3),
    [interesting(0.9),axiom,file(seqm_3,fc2_seqm_3)]).

fof(redefinition_k14_seq_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers)
        & v1_xreal_0(B) )
     => k14_seq_1(A,B) = k12_seq_1(A,B) ) ),
    file(seq_1,k14_seq_1),
    [interesting(0.9),axiom,file(seq_1,k14_seq_1)]).

fof(redefinition_k2_seq_1,definition,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seq_1,k2_seq_1),
    [interesting(0.9),axiom,file(seq_1,k2_seq_1)]).

fof(redefinition_k2_seq_2,definition,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => k2_seq_2(A) = k1_seq_2(A) ) ),
    file(seq_2,k2_seq_2),
    [interesting(0.9),axiom,file(seq_2,k2_seq_2)]).

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

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ),
    file(seq_1,k2_seq_1),
    [interesting(0.9),axiom,file(seq_1,k2_seq_1)]).

fof(dt_k2_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k2_seq_2(A),k1_numbers) ) ),
    file(seq_2,k2_seq_2),
    [interesting(0.9),axiom,file(seq_2,k2_seq_2)]).

fof(dh_c4_2_1__ali2,definition,
    ( ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => k2_seq_1(k5_numbers,k1_numbers,A,B) = k4_power(c3_2__ali2,k1_nat_1(B,1)) ) )
   => ( v1_funct_1(c4_2_1__ali2)
      & v1_funct_2(c4_2_1__ali2,k5_numbers,k1_numbers)
      & m2_relset_1(c4_2_1__ali2,k5_numbers,k1_numbers)
      & ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => k2_seq_1(k5_numbers,k1_numbers,c4_2_1__ali2,C) = k4_power(c3_2__ali2,k1_nat_1(C,1)) ) ) ),
    introduced(definition,[new_symbol(c4_2_1__ali2),file(ali2,c4_2_1__ali2)]),
    [interesting(0.65),axiom,file(ali2,c4_2_1__ali2)]).

fof(s1_seq_1__e12_2_1__ali2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ? [B] : 
          ( v1_funct_1(B)
          & v1_funct_2(B,k5_numbers,k1_numbers)
          & m2_relset_1(B,k5_numbers,k1_numbers)
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k2_seq_1(k5_numbers,k1_numbers,B,C) = k4_power(A,k1_nat_1(C,1)) ) ) ) ),
    file(ali2,s1_seq_1__e12_2_1__ali2),
    [interesting(0.9),axiom,file(ali2,s1_seq_1__e12_2_1__ali2)]).

fof(e12_2_1__ali2,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k1_numbers)
      & m2_relset_1(A,k5_numbers,k1_numbers)
      & ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_seq_1(k5_numbers,k1_numbers,A,B) = k4_power(c3_2__ali2,k1_nat_1(B,1)) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc3_xreal_0,fc8_xreal_0,rc1_membered,rc1_xreal_0,commutativity_k2_xcmplx_0,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_power,dt_k5_ordinal2,dt_m1_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k2_seq_1,redefinition_k4_power,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_power,dt_k5_numbers,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c3_2__ali2,fc2_membered,spc1_numerals,spc1_boole,s1_seq_1__e12_2_1__ali2]),
    [interesting(0.65),file(ali2,e12_2_1__ali2),[file(ali2,e12_2_1__ali2)]]).

fof(dt_c4_2_1__ali2,plain,
    ( v1_funct_1(c4_2_1__ali2)
    & v1_funct_2(c4_2_1__ali2,k5_numbers,k1_numbers)
    & m2_relset_1(c4_2_1__ali2,k5_numbers,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[dh_c4_2_1__ali2,e12_2_1__ali2]),
    [interesting(0.65),file(ali2,c4_2_1__ali2),[file(ali2,c4_2_1__ali2)]]).

fof(de_c6_2_1__ali2,definition,(
    c6_2_1__ali2 = k2_funcop_1(k5_numbers,k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2))) ),
    introduced(definition,[new_symbol(c6_2_1__ali2),file(ali2,c6_2_1__ali2)]),
    [interesting(0.65),axiom,file(ali2,c6_2_1__ali2)]).

fof(t57_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,B)
     => ( v1_funct_1(k2_funcop_1(A,C))
        & v1_funct_2(k2_funcop_1(A,C),A,B)
        & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ),
    file(funcop_1,t57_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t57_funcop_1)]).

fof(e17_2_1__ali2,plain,
    ( v1_funct_1(k2_funcop_1(k5_numbers,k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2))))
    & v1_funct_2(k2_funcop_1(k5_numbers,k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2))),k5_numbers,k1_numbers)
    & m2_relset_1(k2_funcop_1(k5_numbers,k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2))),k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_pcomps_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc4_seqm_3,cc7_xreal_0,fc3_pcomps_1,fc4_ordinal2,fc4_pcomps_1,fc6_membered,rc1_membered,rc1_xreal_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_c2_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_seqm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k4_metric_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k2_funcop_1,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,de_c3_2_1__ali2,fc2_membered,fc2_seqm_3,t1_subset,t7_boole,t57_funcop_1]),
    [interesting(0.65),file(ali2,e17_2_1__ali2),[file(ali2,e17_2_1__ali2)]]).

fof(dt_c6_2_1__ali2,plain,
    ( v1_funct_1(c6_2_1__ali2)
    & v1_funct_2(c6_2_1__ali2,k5_numbers,k1_numbers)
    & m2_relset_1(c6_2_1__ali2,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_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,dt_k5_pcomps_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc4_seqm_3,cc7_xreal_0,fc3_pcomps_1,fc4_ordinal2,fc4_pcomps_1,fc6_membered,rc1_membered,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_c2_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_seqm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_m2_relset_1,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k2_funcop_1,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,de_c3_2_1__ali2,fc2_membered,fc2_seqm_3,de_c6_2_1__ali2,e17_2_1__ali2]),
    [interesting(0.65),file(ali2,c6_2_1__ali2),[file(ali2,c6_2_1__ali2)]]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t13_funcop_1)]).

fof(e18_2_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,A) = k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2)) ) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_pcomps_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc4_seqm_3,cc7_xreal_0,fc3_pcomps_1,fc4_ordinal2,fc4_pcomps_1,fc4_subset_1,fc6_membered,rc1_membered,rc1_xreal_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c2_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_seqm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k4_metric_1,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_funcop_1,dt_k2_seq_1,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,dt_c6_2_1__ali2,de_c3_2_1__ali2,de_c6_2_1__ali2,fc2_membered,fc2_seqm_3,t1_subset,t7_boole,t13_funcop_1]),
    [interesting(0.65),file(ali2,e18_2_1__ali2),[file(ali2,e18_2_1__ali2)]]).

fof(e22_2_1__ali2,plain,(
    k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,0) = k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc1_xreal_0,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_pcomps_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_seqm_3,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc3_pcomps_1,fc4_ordinal2,fc4_pcomps_1,fc4_subset_1,fc6_membered,rc1_membered,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_metric_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c2_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc2_seqm_3,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_m2_subset_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,dt_c6_2_1__ali2,de_c3_2_1__ali2,de_c6_2_1__ali2,fc2_membered,spc0_numerals,spc0_boole,e18_2_1__ali2]),
    [interesting(0.65),file(ali2,e22_2_1__ali2),[file(ali2,e22_2_1__ali2)]]).

fof(e13_2_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_seq_1(k5_numbers,k1_numbers,c4_2_1__ali2,A) = k4_power(c3_2__ali2,k1_nat_1(A,1)) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[dh_c4_2_1__ali2,e12_2_1__ali2]),
    [interesting(0.65),file(ali2,e13_2_1__ali2),[file(ali2,e13_2_1__ali2)]]).

fof(t1_series_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k8_funct_2(k5_numbers,k1_numbers,B,C) = k3_power(A,k1_nat_1(C,1)) )
           => ( r1_xreal_0(A,0)
              | r1_xreal_0(1,A)
              | ( v4_seq_2(B)
                & k2_seq_2(B) = 0 ) ) ) ) ) ),
    file(series_1,t1_series_1),
    [interesting(0.9),axiom,file(series_1,t1_series_1)]).

fof(e14_2_1__ali2,plain,
    ( v4_seq_2(c4_2_1__ali2)
    & k2_seq_2(c4_2_1__ali2) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,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,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc3_xreal_0,fc4_subset_1,fc5_membered,fc8_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,spc6_arithm,t1_arithm,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k4_power,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_seq_1,dt_k2_seq_2,dt_k3_power,dt_k4_power,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_m2_subset_1,dt_c3_2__ali2,dt_c4_2_1__ali2,cc2_xreal_0,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_2__ali2,e13_2_1__ali2,t1_series_1,rqLessOrEqual__r1_xreal_0__r1_r0]),
    [interesting(0.65),file(ali2,e14_2_1__ali2),[file(ali2,e14_2_1__ali2)]]).

fof(t22_seq_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v4_seq_2(B)
           => k2_seq_2(k14_seq_1(B,A)) = k3_xcmplx_0(A,k2_seq_2(B)) ) ) ) ),
    file(seq_2,t22_seq_2),
    [interesting(0.9),axiom,file(seq_2,t22_seq_2)]).

fof(e1_2_1_3__ali2,plain,(
    k2_seq_2(k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)))) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_subset_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,existence_m2_relset_1,redefinition_k14_seq_1,redefinition_k2_seq_2,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,cc2_xreal_0,fc2_membered,fc4_xreal_0,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,e14_2_1__ali2,t22_seq_2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ali2,e1_2_1_3__ali2),[file(ali2,e1_2_1_3__ali2)]]).

fof(e2_2_1_3__ali2,plain,(
    k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),0) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc4_subset_1,fc4_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,spc7_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,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,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ali2,e2_2_1_3__ali2),[file(ali2,e2_2_1_3__ali2)]]).

fof(e16_2_1__ali2,plain,(
    k2_seq_2(k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)))) = 0 ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2])],[e1_2_1_3__ali2,e2_2_1_3__ali2]),
    [interesting(0.65),file(ali2,e16_2_1__ali2),[file(ali2,e16_2_1__ali2)]]).

fof(dh_c1_2_1_4__ali2,definition,
    ( ( m2_subset_1(c1_2_1_4__ali2,k1_numbers,k5_numbers)
     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,c1_2_1_4__ali2),k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),c1_2_1_4__ali2)) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,A),k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),A)) ) ),
    introduced(definition,[new_symbol(c1_2_1_4__ali2),file(ali2,c1_2_1_4__ali2)]),
    [interesting(0.5),axiom,file(ali2,c1_2_1_4__ali2)]).

fof(dt_c1_2_1_4__ali2,assumption,(
    m2_subset_1(c1_2_1_4__ali2,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(ali2,c1_2_1_4__ali2)]),
    [interesting(0.5),axiom,file(ali2,c1_2_1_4__ali2)]).

fof(t13_seq_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,k1_numbers)
                & m2_relset_1(C,k5_numbers,k1_numbers) )
             => ( B = k14_seq_1(C,A)
              <=> ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k2_seq_1(k5_numbers,k1_numbers,B,D) = k3_xcmplx_0(A,k2_seq_1(k5_numbers,k1_numbers,C,D)) ) ) ) ) ) ),
    file(seq_1,t13_seq_1),
    [interesting(0.9),axiom,file(seq_1,t13_seq_1)]).

fof(e1_2_1_4_1__ali2,plain,(
    k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),c1_2_1_4__ali2) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k2_seq_1(k5_numbers,k1_numbers,c4_2_1__ali2,c1_2_1_4__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc4_subset_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc7_arithm,t2_subset,t3_arithm,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,cc2_xreal_0,fc2_membered,fc4_xreal_0,spc1_numerals,spc1_boole,t13_seq_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e1_2_1_4_1__ali2),[file(ali2,e1_2_1_4_1__ali2)]]).

fof(e2_2_1_4_1__ali2,plain,(
    k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k2_seq_1(k5_numbers,k1_numbers,c4_2_1__ali2,c1_2_1_4__ali2)) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,k1_nat_1(c1_2_1_4__ali2,1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_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,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_subset_1,fc4_xreal_0,fc6_membered,fc8_xreal_0,rc1_membered,rc1_xreal_0,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,fc2_membered,spc1_numerals,spc1_boole,e13_2_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.35),file(ali2,e2_2_1_4_1__ali2),[file(ali2,e2_2_1_4_1__ali2)]]).

fof(e5_2_1_4__ali2,plain,(
    k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),c1_2_1_4__ali2) = k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,k1_nat_1(c1_2_1_4__ali2,1))) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_2_1_4__ali2,dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,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,fc4_subset_1,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k3_xcmplx_0,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_membered,fc8_xreal_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,redefinition_k14_seq_1,redefinition_k1_nat_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,dt_k14_seq_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,fc2_membered,spc1_numerals,spc1_boole,e1_2_1_4_1__ali2,e2_2_1_4_1__ali2]),
    [interesting(0.5),file(ali2,e5_2_1_4__ali2),[file(ali2,e5_2_1_4__ali2)]]).

fof(s7_domain_1__e1_2_1_4__ali2,theorem,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A)
        & m1_ali2(B,A)
        & m1_subset_1(C,k1_numbers)
        & m1_subset_1(D,u1_struct_0(A))
        & m2_subset_1(E,k1_numbers,k5_numbers) )
     => m1_subset_1(a_5_1_ali2(A,B,C,D,E),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(ali2,s7_domain_1__e1_2_1_4__ali2),
    [interesting(0.9),axiom,file(ali2,s7_domain_1__e1_2_1_4__ali2)]).

fof(e1_2_1_4__ali2,plain,(
    m1_subset_1(a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_4__ali2),k1_zfmisc_1(u1_struct_0(c1_2__ali2))) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[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,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,dt_k1_funct_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_power,dt_k3_xcmplx_0,dt_m1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_subset_1,fc4_xreal_0,fc8_xreal_0,rc1_xreal_0,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_nat_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_struct_0,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,spc1_numerals,spc1_boole,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_metric_1,dt_m1_ali2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t2_tarski,fraenkel_a_5_1_ali2,s7_domain_1__e1_2_1_4__ali2]),
    [interesting(0.5),file(ali2,e1_2_1_4__ali2),[file(ali2,e1_2_1_4__ali2)]]).

fof(e2_2_1_4__ali2,plain,(
    r2_hidden(a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_4__ali2),c1_2_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dt_k2_zfmisc_1,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,fc4_subset_1,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_m1_relset_1,dt_m2_relset_1,dt_u1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc6_membered,fc8_xreal_0,rc1_xreal_0,spc5_arithm,spc6_arithm,t1_real,t4_real,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,abstractness_v1_pre_topc,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k1_nat_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_ordinal2,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_struct_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc7_arithm,t2_subset,t3_arithm,t5_subset,t6_boole,t8_boole,free_g1_pre_topc,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_g1_pre_topc,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_xcmplx_0,dt_k4_pcomps_1,dt_k5_numbers,dt_k5_pcomps_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c4_2__ali2,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,t1_subset,t3_subset,t4_subset,t7_boole,t2_tarski,fraenkel_a_5_0_ali2,fraenkel_a_5_1_ali2,spc1_numerals,spc1_boole,e1_2_1_4__ali2,e3_2_1__ali2,e4_2_1__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ali2,e2_2_1_4__ali2),[file(ali2,e2_2_1_4__ali2)]]).

fof(e10_2_1__ali2,plain,(
    r2_hidden(c2_2_1__ali2,k6_setfam_1(u1_struct_0(k5_pcomps_1(c1_2__ali2)),c1_2_1__ali2)) ),
    inference(consider,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c2_2_1__ali2,e9_2_1__ali2]),
    [interesting(0.65),file(ali2,e10_2_1__ali2),[file(ali2,e10_2_1__ali2)]]).

fof(d1_setfam_1,definition,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d1_setfam_1)]).

fof(e3_2_1_4__ali2,plain,(
    r2_hidden(c3_2_1__ali2,a_5_1_ali2(c1_2__ali2,c2_2__ali2,c3_2__ali2,c4_2__ali2,c1_2_1_4__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_k2_zfmisc_1,dt_u1_pre_topc,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,fc4_subset_1,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_ordinal2,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc5_membered,fc8_xreal_0,rc1_xreal_0,spc5_arithm,spc6_arithm,t1_real,t4_real,commutativity_k1_nat_1,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_ali2,existence_m1_subset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_ali2,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc2_membered,fc3_pcomps_1,fc4_pcomps_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rqLessOrEqual__r1_xreal_0__r1_r1,spc7_arithm,t2_subset,t3_arithm,t3_subset,t4_subset,t5_subset,t8_boole,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,redefinition_k6_setfam_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k3_xcmplx_0,dt_k5_pcomps_1,dt_k6_setfam_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c2_2_1__ali2,dt_c3_2__ali2,dt_c3_2_1__ali2,dt_c4_2__ali2,de_c3_2_1__ali2,fc6_membered,t1_subset,t6_boole,t7_boole,t2_tarski,fraenkel_a_5_1_ali2,spc1_numerals,spc1_boole,e2_2_1_4__ali2,e10_2_1__ali2,d1_setfam_1,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ali2,e3_2_1_4__ali2),[file(ali2,e3_2_1_4__ali2)]]).

fof(e4_2_1_4__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & c3_2_1__ali2 = A
      & r1_xreal_0(k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)),k4_real_1(k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)),k4_power(c3_2__ali2,k1_nat_1(c1_2_1_4__ali2,1)))) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_k2_zfmisc_1,dt_l1_pre_topc,cc1_xreal_0,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_pcomps_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,dt_c2_2_1__ali2,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_xreal_0,rc3_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t8_boole,commutativity_k1_nat_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k1_nat_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k1_nat_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1__ali2,dt_c4_2__ali2,de_c3_2_1__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,t2_tarski,fraenkel_a_5_1_ali2,spc1_numerals,spc1_boole,e3_2_1_4__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.5),file(ali2,e4_2_1_4__ali2),[file(ali2,e4_2_1_4__ali2)]]).

fof(e6_2_1_4__ali2,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,c1_2_1_4__ali2),k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),c1_2_1_4__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc1_xreal_0,cc4_seqm_3,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_pcomps_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_seqm_3,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,fc3_pcomps_1,fc4_ordinal2,fc4_pcomps_1,fc4_subset_1,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_membered,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,commutativity_k2_xcmplx_0,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_metric_1,dt_k2_xcmplx_0,dt_k3_power,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_relset_1,dt_c2_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc13_xreal_0,fc17_xreal_0,fc18_xreal_0,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_xreal_0,fc23_xreal_0,fc2_seqm_3,fc3_xreal_0,fc4_xreal_0,fc5_membered,fc5_xreal_0,fc8_xreal_0,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,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,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k14_seq_1,redefinition_k1_nat_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k4_power,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k14_seq_1,dt_k1_nat_1,dt_k1_numbers,dt_k2_seq_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_power,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k6_xcmplx_0,dt_k8_funct_2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c3_2_1__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,dt_c6_2_1__ali2,de_c3_2_1__ali2,de_c6_2_1__ali2,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealNeg__k4_xcmplx_0__r0_r0,t1_numerals,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e5_2_1_4__ali2,e18_2_1__ali2,e4_2_1_4__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1]),
    [interesting(0.5),file(ali2,e6_2_1_4__ali2),[file(ali2,e6_2_1_4__ali2)]]).

fof(i2_2_1_4__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i2_2_1_4__ali2)]),
    [interesting(0.5),trivial,file(ali2,i2_2_1_4__ali2)]).

fof(i1_2_1_4__ali2,plain,(
    r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,c1_2_1_4__ali2),k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),c1_2_1_4__ali2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1_4__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc1_xreal_0,dt_k2_zfmisc_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc4_subset_1,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_1,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c1_2_1_4__ali2,dt_c2_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,dt_c6_2_1__ali2,fc2_membered,e6_2_1_4__ali2,i2_2_1_4__ali2]),
    [interesting(0.5),file(ali2,i1_2_1_4__ali2),[file(ali2,i1_2_1_4__ali2)]]).

fof(i1_2_1_4_tmp__ali2,plain,
    ( m2_subset_1(c1_2_1_4__ali2,k1_numbers,k5_numbers)
   => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,c1_2_1_4__ali2),k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),c1_2_1_4__ali2)) ),
    inference(discharge_asm,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c1_2_1_4__ali2])],[dt_c1_2_1_4__ali2,i1_2_1_4__ali2]),
    [interesting(0.65),e20_2_1__ali2]).

fof(e20_2_1__ali2,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,c6_2_1__ali2,A),k2_seq_1(k5_numbers,k1_numbers,k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))),A)) ) ),
    inference(let,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[i1_2_1_4_tmp__ali2,dh_c1_2_1_4__ali2]),
    [interesting(0.65),file(ali2,e20_2_1__ali2),[file(ali2,e20_2_1__ali2)]]).

fof(t21_seq_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( v4_seq_2(B)
           => v4_seq_2(k14_seq_1(B,A)) ) ) ) ),
    file(seq_2,t21_seq_2),
    [interesting(0.9),axiom,file(seq_2,t21_seq_2)]).

fof(e15_2_1__ali2,plain,(
    v4_seq_2(k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__ali2,dt_c2_2__ali2])],[cc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc4_subset_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_m2_relset_1,redefinition_k14_seq_1,redefinition_k2_seq_2,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_2,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,cc2_xreal_0,fc2_membered,spc0_numerals,spc0_boole,e14_2_1__ali2,t21_seq_2]),
    [interesting(0.65),file(ali2,e15_2_1__ali2),[file(ali2,e15_2_1__ali2)]]).

fof(t39_seq_4,theorem,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v5_seqm_3(A)
       => v4_seq_2(A) ) ) ),
    file(seq_4,t39_seq_4),
    [interesting(0.9),axiom,file(seq_4,t39_seq_4)]).

fof(e19_2_1__ali2,plain,(
    v4_seq_2(c6_2_1__ali2) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,dt_k5_pcomps_1,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc3_pcomps_1,fc4_pcomps_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,dt_k1_funct_1,dt_k1_xboole_0,dt_k2_metric_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_c2_2_1__ali2,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc4_seqm_3,cc7_xreal_0,fc1_struct_0,fc4_ordinal2,fc6_membered,rc1_membered,rc1_xreal_0,rc3_struct_0,rc5_struct_0,t1_subset,t4_subset,t5_subset,commutativity_k4_metric_1,existence_m1_relset_1,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k4_metric_1,dt_k5_ordinal2,dt_k8_funct_2,dt_m1_relset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,de_c3_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_seqm_3,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_seqm_3,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_relset_1,dt_c6_2_1__ali2,de_c6_2_1__ali2,fc2_membered,t39_seq_4]),
    [interesting(0.65),file(ali2,e19_2_1__ali2),[file(ali2,e19_2_1__ali2)]]).

fof(t32_seq_2,theorem,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( v4_seq_2(A)
              & v4_seq_2(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,B,C)) ) )
           => r1_xreal_0(k2_seq_2(A),k2_seq_2(B)) ) ) ) ),
    file(seq_2,t32_seq_2),
    [interesting(0.9),axiom,file(seq_2,t32_seq_2)]).

fof(e21_2_1__ali2,plain,(
    r1_xreal_0(k2_seq_2(c6_2_1__ali2),k2_seq_2(k14_seq_1(c4_2_1__ali2,k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2))))) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,dt_k5_pcomps_1,cc1_xreal_0,cc4_seqm_3,fc3_pcomps_1,fc4_pcomps_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c2_2_1__ali2,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_seqm_3,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc4_ordinal2,fc6_membered,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t1_subset,t2_real,t3_real,t4_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_c3_2_1__ali2,de_c3_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc2_xreal_0,cc4_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc2_seqm_3,fc4_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k14_seq_1,dt_k1_numbers,dt_k2_seq_1,dt_k2_seq_2,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,dt_c6_2_1__ali2,de_c6_2_1__ali2,fc2_membered,e20_2_1__ali2,e15_2_1__ali2,e19_2_1__ali2,t32_seq_2]),
    [interesting(0.65),file(ali2,e21_2_1__ali2),[file(ali2,e21_2_1__ali2)]]).

fof(t40_seq_4,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
         => ( ( ( v5_seqm_3(B)
                & r2_hidden(A,k2_relat_1(B)) )
              | ( v5_seqm_3(B)
                & ? [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                    & k8_funct_2(k5_numbers,k1_numbers,B,C) = A ) ) )
           => k2_seq_2(B) = A ) ) ) ),
    file(seq_4,t40_seq_4),
    [interesting(0.9),axiom,file(seq_4,t40_seq_4)]).

fof(e23_2_1__ali2,plain,
    ( r1_xreal_0(k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2)),0)
    & r1_xreal_0(0,k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_l1_pre_topc,cc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_pcomps_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_seqm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc3_pcomps_1,fc4_ordinal2,fc4_pcomps_1,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,dt_k12_seq_1,dt_k1_funct_1,dt_k1_seq_2,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_metric_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_c2_2_1__ali2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_seqm_3,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc2_seqm_3,fc4_subset_1,fc5_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc3_struct_0,rc5_struct_0,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_l1_metric_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k14_seq_1,redefinition_k2_seq_1,redefinition_k2_seq_2,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k14_seq_1,dt_k1_numbers,dt_k2_relat_1,dt_k2_seq_1,dt_k2_seq_2,dt_k4_metric_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_metric_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,dt_c4_2__ali2,dt_c4_2_1__ali2,dt_c6_2_1__ali2,de_c3_2_1__ali2,de_c6_2_1__ali2,cc2_xreal_0,fc2_membered,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,t1_subset,t7_boole,spc0_numerals,spc0_boole,e22_2_1__ali2,e16_2_1__ali2,e21_2_1__ali2,t5_metric_1,t40_seq_4]),
    [interesting(0.65),file(ali2,e23_2_1__ali2),[file(ali2,e23_2_1__ali2)]]).

fof(e24_2_1__ali2,plain,(
    k4_metric_1(c1_2__ali2,c3_2_1__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c3_2_1__ali2)) = 0 ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_k2_zfmisc_1,dt_l1_pre_topc,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_pcomps_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_c2_2_1__ali2,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k8_funct_2,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,de_c3_2_1__ali2,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,e23_2_1__ali2]),
    [interesting(0.65),file(ali2,e24_2_1__ali2),[file(ali2,e24_2_1__ali2)]]).

fof(e25_2_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)) = 0 ) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[free_g1_pre_topc,dt_g1_pre_topc,dt_u1_pre_topc,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,abstractness_v1_pre_topc,existence_l1_pre_topc,dt_k2_zfmisc_1,dt_l1_pre_topc,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_pcomps_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc3_pcomps_1,fc4_pcomps_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,dt_c2_2_1__ali2,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2_1__ali2,de_c3_2_1__ali2,spc0_numerals,spc0_boole,e24_2_1__ali2]),
    [interesting(0.65),file(ali2,e25_2_1__ali2),[file(ali2,e25_2_1__ali2)]]).

fof(i2_2_1__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i2_2_1__ali2)]),
    [interesting(0.65),trivial,file(ali2,i2_2_1__ali2)]).

fof(i1_2_1__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)) = 0 ) ),
    inference(conclusion,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e25_2_1__ali2,i2_2_1__ali2]),
    [interesting(0.65),file(ali2,i1_2_1__ali2),[file(ali2,i1_2_1__ali2)]]).

fof(e6_2__ali2,plain,(
    ~ ( k4_metric_1(c1_2__ali2,c4_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c4_2__ali2)) != 0
      & ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
         => k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)) != 0 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e1_2_1__ali2])],[e1_2_1__ali2,i1_2_1__ali2]),
    [interesting(0.8),file(ali2,e6_2__ali2),[file(ali2,e6_2__ali2)]]).

fof(e7_2__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & k4_metric_1(c1_2__ali2,A,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A)) = 0 ) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k4_metric_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c4_2__ali2,spc0_numerals,spc0_boole,e6_2__ali2]),
    [interesting(0.8),file(ali2,e7_2__ali2),[file(ali2,e7_2__ali2)]]).

fof(dt_c6_2__ali2,plain,(
    m1_subset_1(c6_2__ali2,u1_struct_0(c1_2__ali2)) ),
    inference(consider,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c6_2__ali2,e7_2__ali2]),
    [interesting(0.8),file(ali2,c6_2__ali2),[file(ali2,c6_2__ali2)]]).

fof(e8_2__ali2,plain,(
    k4_metric_1(c1_2__ali2,c6_2__ali2,k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c6_2__ali2)) = 0 ),
    inference(consider,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[dh_c6_2__ali2,e7_2__ali2]),
    [interesting(0.8),file(ali2,e8_2__ali2),[file(ali2,e8_2__ali2)]]).

fof(t2_metric_1,theorem,(
    ! [A] : 
      ( l1_metric_1(A)
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k2_metric_1(A,B,C) = 0
                 => B = C ) ) )
      <=> v7_metric_1(A) ) ) ),
    file(metric_1,t2_metric_1),
    [interesting(0.9),axiom,file(metric_1,t2_metric_1)]).

fof(e9_2__ali2,plain,(
    k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c6_2__ali2) = c6_2__ali2 ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_xreal_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k5_numbers,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_l1_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k8_funct_2,dt_k2_metric_1,dt_k4_metric_1,dt_k8_funct_2,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c6_2__ali2,spc0_numerals,spc0_boole,e8_2__ali2,t2_metric_1]),
    [interesting(0.8),file(ali2,e9_2__ali2),[file(ali2,e9_2__ali2)]]).

fof(dh_c7_2__ali2,definition,
    ( ( m1_subset_1(c7_2__ali2,u1_struct_0(c1_2__ali2))
     => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c7_2__ali2) = c7_2__ali2
       => c7_2__ali2 = c6_2__ali2 ) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
       => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
         => A = c6_2__ali2 ) ) ),
    introduced(definition,[new_symbol(c7_2__ali2),file(ali2,c7_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c7_2__ali2)]).

fof(e10_2__ali2,assumption,(
    k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c7_2__ali2) = c7_2__ali2 ),
    introduced(assumption,[file(ali2,e10_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,e10_2__ali2)]).

fof(e11_2__ali2,assumption,(
    c7_2__ali2 != c6_2__ali2 ),
    introduced(assumption,[file(ali2,e11_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,e11_2__ali2)]).

fof(dt_c7_2__ali2,assumption,(
    m1_subset_1(c7_2__ali2,u1_struct_0(c1_2__ali2)) ),
    introduced(assumption,[file(ali2,c7_2__ali2)]),
    [interesting(0.8),axiom,file(ali2,c7_2__ali2)]).

fof(e13_2__ali2,plain,(
    r1_xreal_0(0,k4_metric_1(c1_2__ali2,c7_2__ali2,c6_2__ali2)) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c7_2__ali2])],[reflexivity_r1_tarski,cc1_xreal_0,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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_struct_0,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_l1_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,dt_k4_metric_1,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c6_2__ali2,dt_c7_2__ali2,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_numerals,spc0_boole,t5_metric_1]),
    [interesting(0.8),file(ali2,e13_2__ali2),[file(ali2,e13_2__ali2)]]).

fof(e12_2__ali2,plain,(
    k4_metric_1(c1_2__ali2,c7_2__ali2,c6_2__ali2) != 0 ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c7_2__ali2,e11_2__ali2])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,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,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_l1_struct_0,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_metric_1,existence_l1_metric_1,existence_m1_subset_1,redefinition_k4_metric_1,dt_k2_metric_1,dt_k4_metric_1,dt_l1_metric_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c6_2__ali2,dt_c7_2__ali2,spc0_numerals,spc0_boole,e11_2__ali2,t2_metric_1]),
    [interesting(0.8),file(ali2,e12_2__ali2),[file(ali2,e12_2__ali2)]]).

fof(t145_real_2,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,0)
                  & ~ r1_xreal_0(1,B) )
                | ( ~ r1_xreal_0(0,A)
                  & ~ r1_xreal_0(B,1) ) )
              & r1_xreal_0(A,k3_xcmplx_0(A,B)) ) ) ) ),
    file(real_2,t145_real_2),
    [interesting(0.9),axiom,file(real_2,t145_real_2)]).

fof(e14_2__ali2,plain,(
    ~ r1_xreal_0(k4_metric_1(c1_2__ali2,c7_2__ali2,c6_2__ali2),k4_real_1(c3_2__ali2,k4_metric_1(c1_2__ali2,c7_2__ali2,c6_2__ali2))) ),
    inference(mizar_by,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,dt_c7_2__ali2,e11_2__ali2])],[reflexivity_r1_tarski,cc1_xreal_0,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_struct_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc2_membered,rc1_xreal_0,spc7_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k4_metric_1,redefinition_k4_real_1,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_c1_2__ali2,dt_c3_2__ali2,dt_c6_2__ali2,dt_c7_2__ali2,cc2_xreal_0,fc4_xreal_0,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,e13_2__ali2,e2_2__ali2,e12_2__ali2,t145_real_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r1]),
    [interesting(0.8),file(ali2,e14_2__ali2),[file(ali2,e14_2__ali2)]]).

fof(e15_2__ali2,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c7_2__ali2,e11_2__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e10_2__ali2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_xreal_0,fc4_subset_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc1_ordinal2,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_l1_metric_1,existence_l1_struct_0,existence_m1_ali2,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_metric_1,dt_k5_numbers,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,dt_m2_subset_1,cc15_membered,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_struct_0,fc23_xreal_0,fc2_membered,fc4_xreal_0,rc1_xreal_0,rc3_struct_0,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k3_xcmplx_0,commutativity_k4_metric_1,commutativity_k4_real_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,redefinition_k4_metric_1,redefinition_k4_real_1,redefinition_k8_funct_2,dt_k3_xcmplx_0,dt_k4_metric_1,dt_k4_real_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c3_2__ali2,dt_c6_2__ali2,dt_c7_2__ali2,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_numerals,spc1_boole,e14_2__ali2,e3_2__ali2,e9_2__ali2,e10_2__ali2,rqRealMult__k3_xcmplx_0__r1_r1_r1]),
    [interesting(0.8),file(ali2,e15_2__ali2),[file(ali2,e15_2__ali2)]]).

fof(i9_2__ali2,theorem,(
    $true ),
    introduced(tautology,[file(ali2,i9_2__ali2)]),
    [interesting(0.8),trivial,file(ali2,i9_2__ali2)]).

fof(i8_2__ali2,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c7_2__ali2,e11_2__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e10_2__ali2])],[e15_2__ali2,i9_2__ali2]),
    [interesting(0.8),file(ali2,i8_2__ali2),[file(ali2,i8_2__ali2)]]).

fof(i7_2__ali2,plain,(
    c7_2__ali2 = c6_2__ali2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c7_2__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2,e10_2__ali2]),discharge_asm(discharge,[e11_2__ali2])],[e11_2__ali2,i8_2__ali2]),
    [interesting(0.8),file(ali2,i7_2__ali2),[file(ali2,i7_2__ali2)]]).

fof(i6_2__ali2,plain,
    ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c7_2__ali2) = c7_2__ali2
   => c7_2__ali2 = c6_2__ali2 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c7_2__ali2,e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e10_2__ali2])],[e10_2__ali2,i7_2__ali2]),
    [interesting(0.8),file(ali2,i6_2__ali2),[file(ali2,i6_2__ali2)]]).

fof(i6_2_tmp__ali2,plain,
    ( m1_subset_1(c7_2__ali2,u1_struct_0(c1_2__ali2))
   => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c7_2__ali2) = c7_2__ali2
     => c7_2__ali2 = c6_2__ali2 ) ),
    inference(discharge_asm,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[dt_c7_2__ali2])],[dt_c7_2__ali2,i6_2__ali2]),
    [interesting(0.8),i5_2__ali2]).

fof(i5_2__ali2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
     => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
       => A = c6_2__ali2 ) ) ),
    inference(let,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[i6_2_tmp__ali2,dh_c7_2__ali2]),
    [interesting(0.8),file(ali2,i5_2__ali2),[file(ali2,i5_2__ali2)]]).

fof(i4_2__ali2,plain,
    ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,c6_2__ali2) = c6_2__ali2
    & ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
       => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
         => A = c6_2__ali2 ) ) ),
    inference(conclusion,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[e9_2__ali2,i5_2__ali2]),
    [interesting(0.8),file(ali2,i4_2__ali2),[file(ali2,i4_2__ali2)]]).

fof(i3_2__ali2,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
      & k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
         => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B) = B
           => B = A ) ) ) ),
    inference(take,[status(thm),assumptions([e4_2__ali2,dt_c2_2__ali2,dt_c1_2__ali2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_xreal_0,cc20_membered,cc2_xreal_0,cc7_xreal_0,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,redefinition_m2_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,dt_k1_funct_1,dt_l1_metric_1,dt_l1_struct_0,dt_m1_ali2,dt_m1_relset_1,cc15_membered,fc1_struct_0,rc3_struct_0,redefinition_k8_funct_2,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__ali2,dt_c2_2__ali2,dt_c6_2__ali2,i4_2__ali2]),
    [interesting(0.8),file(ali2,i3_2__ali2),[file(ali2,i3_2__ali2)]]).

fof(i2_2__ali2,plain,(
    ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
      & ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
         => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
              & ! [B] : 
                  ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
                 => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B) = B
                   => B = A ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__ali2,dt_c1_2__ali2]),discharge_asm(discharge,[e4_2__ali2])],[e4_2__ali2,i3_2__ali2]),
    [interesting(0.8),file(ali2,i2_2__ali2),[file(ali2,i2_2__ali2)]]).

fof(i2_2_tmp__ali2,plain,
    ( m1_ali2(c2_2__ali2,c1_2__ali2)
   => ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
        & ! [A] : 
            ( m1_subset_1(A,u1_struct_0(c1_2__ali2))
           => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,A) = A
                & ! [B] : 
                    ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
                   => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),c2_2__ali2,B) = B
                     => B = A ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__ali2]),discharge_asm(discharge,[dt_c2_2__ali2])],[dt_c2_2__ali2,i2_2__ali2]),
    [interesting(0.8),i1_2__ali2]).

fof(i1_2__ali2,plain,(
    ! [A] : 
      ( m1_ali2(A,c1_2__ali2)
     => ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
             => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),A,B) = B
                  & ! [C] : 
                      ( m1_subset_1(C,u1_struct_0(c1_2__ali2))
                     => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),A,C) = C
                       => C = B ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__ali2])],[i2_2_tmp__ali2,dh_c2_2__ali2]),
    [interesting(0.8),file(ali2,i1_2__ali2),[file(ali2,i1_2__ali2)]]).

fof(i1_2_tmp__ali2,plain,
    ( ( ~ v3_struct_0(c1_2__ali2)
      & v6_metric_1(c1_2__ali2)
      & v7_metric_1(c1_2__ali2)
      & v8_metric_1(c1_2__ali2)
      & v9_metric_1(c1_2__ali2)
      & l1_metric_1(c1_2__ali2) )
   => ! [A] : 
        ( m1_ali2(A,c1_2__ali2)
       => ~ ( v2_compts_1(k5_pcomps_1(c1_2__ali2))
            & ! [B] : 
                ( m1_subset_1(B,u1_struct_0(c1_2__ali2))
               => ~ ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),A,B) = B
                    & ! [C] : 
                        ( m1_subset_1(C,u1_struct_0(c1_2__ali2))
                       => ( k8_funct_2(u1_struct_0(c1_2__ali2),u1_struct_0(c1_2__ali2),A,C) = C
                         => C = B ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__ali2])],[dt_c1_2__ali2,i1_2__ali2]),
    [interesting(1),t2_ali2]).

fof(t2_ali2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v7_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] : 
          ( m1_ali2(B,A)
         => ~ ( v2_compts_1(k5_pcomps_1(A))
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ~ ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = C
                      & ! [D] : 
                          ( m1_subset_1(D,u1_struct_0(A))
                         => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = D
                           => D = C ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__ali2,dh_c1_2__ali2]),
    [interesting(1),file(ali2,t2_ali2),[file(ali2,t2_ali2)]]).