% Mizar ND problem: t9_jordan2c,jordan2c,168,25 
fof(dh_c1_7__jordan2c,definition,
    ( ( m2_subset_1(c1_7__jordan2c,k1_numbers,k5_numbers)
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(k15_euclid(c1_7__jordan2c)))
                 => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,A,B),C) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,A,C),B) ) ) ) )
   => ! [D] : 
        ( m2_subset_1(D,k1_numbers,k5_numbers)
       => ! [E] : 
            ( m1_subset_1(E,u1_struct_0(k15_euclid(D)))
           => ! [F] : 
                ( m1_subset_1(F,u1_struct_0(k15_euclid(D)))
               => ! [G] : 
                    ( m1_subset_1(G,u1_struct_0(k15_euclid(D)))
                   => k20_euclid(D,k17_euclid(D,E,F),G) = k17_euclid(D,k20_euclid(D,E,G),F) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_7__jordan2c),file(jordan2c,c1_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c1_7__jordan2c)]).

fof(dh_c2_7__jordan2c,definition,
    ( ( m1_subset_1(c2_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c)))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
             => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,A),B) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,B),A) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,u1_struct_0(k15_euclid(c1_7__jordan2c)))
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(k15_euclid(c1_7__jordan2c)))
           => ! [E] : 
                ( m1_subset_1(E,u1_struct_0(k15_euclid(c1_7__jordan2c)))
               => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,C,D),E) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,C,E),D) ) ) ) ),
    introduced(definition,[new_symbol(c2_7__jordan2c),file(jordan2c,c2_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c2_7__jordan2c)]).

fof(dh_c3_7__jordan2c,definition,
    ( ( m1_subset_1(c3_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c)))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
         => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),A) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,A),c3_7__jordan2c) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(k15_euclid(c1_7__jordan2c)))
           => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,B),C) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,C),B) ) ) ),
    introduced(definition,[new_symbol(c3_7__jordan2c),file(jordan2c,c3_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c3_7__jordan2c)]).

fof(dh_c4_7__jordan2c,definition,
    ( ( m1_subset_1(c4_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c)))
     => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),c4_7__jordan2c) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,c4_7__jordan2c),c3_7__jordan2c) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
       => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),A) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,A),c3_7__jordan2c) ) ),
    introduced(definition,[new_symbol(c4_7__jordan2c),file(jordan2c,c4_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c4_7__jordan2c)]).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

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_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(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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k4_finseq_2)]).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_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(dt_u1_metric_1,axiom,(
    ! [A] : 
      ( l1_metric_1(A)
     => ( v1_funct_1(u1_metric_1(A))
        & v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers)
        & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) ) ) ),
    file(metric_1,u1_metric_1),
    [interesting(0.9),axiom,file(metric_1,u1_metric_1)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

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

fof(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(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_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_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc2_finseq_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]).

fof(rc2_finset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_tbsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_metric_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v6_tbsp_1(B,A) ) ) ),
    file(tbsp_1,rc2_tbsp_1),
    [interesting(0.9),axiom,file(tbsp_1,rc2_tbsp_1)]).

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

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_tbsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v6_tbsp_1(B,A) ) ) ),
    file(tbsp_1,rc3_tbsp_1),
    [interesting(0.9),axiom,file(tbsp_1,rc3_tbsp_1)]).

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

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

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(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

fof(free_g1_metric_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
        & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
     => ! [C,D] : 
          ( g1_metric_1(A,B) = g1_metric_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(metric_1,g1_metric_1),
    [interesting(0.9),axiom,file(metric_1,g1_metric_1)]).

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(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(abstractness_v1_metric_1,theorem,(
    ! [A] : 
      ( l1_metric_1(A)
     => ( v1_metric_1(A)
       => A = g1_metric_1(u1_struct_0(A),u1_metric_1(A)) ) ) ),
    file(metric_1,v1_metric_1),
    [interesting(0.9),axiom,file(metric_1,v1_metric_1)]).

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(dt_g1_metric_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers)
        & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) )
     => ( v1_metric_1(g1_metric_1(A,B))
        & l1_metric_1(g1_metric_1(A,B)) ) ) ),
    file(metric_1,g1_metric_1),
    [interesting(0.9),axiom,file(metric_1,g1_metric_1)]).

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_k13_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_funct_1(k13_euclid(A))
        & v1_funct_2(k13_euclid(A),k2_zfmisc_1(k1_euclid(A),k1_euclid(A)),k1_numbers)
        & m2_relset_1(k13_euclid(A),k2_zfmisc_1(k1_euclid(A),k1_euclid(A)),k1_numbers) ) ) ),
    file(euclid,k13_euclid),
    [interesting(0.9),axiom,file(euclid,k13_euclid)]).

fof(dt_k1_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v1_xboole_0(k1_euclid(A))
        & m1_finseq_2(k1_euclid(A),k1_numbers) ) ) ),
    file(euclid,k1_euclid),
    [interesting(0.9),axiom,file(euclid,k1_euclid)]).

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_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_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(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(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_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

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

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

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

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

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

fof(cc2_tbsp_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_metric_1(A)
        & v8_metric_1(A)
        & v9_metric_1(A)
        & l1_metric_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
           => v6_tbsp_1(B,A) ) ) ) ),
    file(tbsp_1,cc2_tbsp_1),
    [interesting(0.9),axiom,file(tbsp_1,cc2_tbsp_1)]).

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

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

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(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_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(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

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

fof(rc1_metric_1,theorem,(
    ? [A] : 
      ( l1_metric_1(A)
      & v1_metric_1(A) ) ),
    file(metric_1,rc1_metric_1),
    [interesting(0.9),axiom,file(metric_1,rc1_metric_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_metric_1,theorem,(
    ? [A] : 
      ( l1_metric_1(A)
      & ~ v3_struct_0(A)
      & v1_metric_1(A) ) ),
    file(metric_1,rc2_metric_1),
    [interesting(0.9),axiom,file(metric_1,rc2_metric_1)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc3_metric_1,theorem,(
    ? [A] : 
      ( l1_metric_1(A)
      & ~ v3_struct_0(A)
      & v1_metric_1(A)
      & v6_metric_1(A)
      & v7_metric_1(A)
      & v8_metric_1(A)
      & v9_metric_1(A) ) ),
    file(metric_1,rc3_metric_1),
    [interesting(0.9),axiom,file(metric_1,rc3_metric_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

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

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

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

fof(d1_euclid,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_euclid(A) = k4_finseq_2(A,k1_numbers) ) ),
    file(euclid,d1_euclid),
    [interesting(0.9),axiom,file(euclid,d1_euclid)]).

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(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(dt_k14_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_metric_1(k14_euclid(A))
        & v6_metric_1(k14_euclid(A))
        & v7_metric_1(k14_euclid(A))
        & v8_metric_1(k14_euclid(A))
        & v9_metric_1(k14_euclid(A))
        & l1_metric_1(k14_euclid(A)) ) ) ),
    file(euclid,k14_euclid),
    [interesting(0.9),axiom,file(euclid,k14_euclid)]).

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

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

fof(dt_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(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_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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(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(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(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

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

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_euclid,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k14_euclid(A))
        & v1_metric_1(k14_euclid(A))
        & v6_metric_1(k14_euclid(A))
        & v7_metric_1(k14_euclid(A))
        & v8_metric_1(k14_euclid(A))
        & v9_metric_1(k14_euclid(A)) ) ) ),
    file(euclid,fc1_euclid),
    [interesting(0.9),axiom,file(euclid,fc1_euclid)]).

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(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(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(rc1_pre_topc,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc1_pre_topc)]).

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(rc2_pcomps_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v3_compts_1(A) ) ),
    file(pcomps_1,rc2_pcomps_1),
    [interesting(0.9),axiom,file(pcomps_1,rc2_pcomps_1)]).

fof(rc2_pre_topc,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc2_pre_topc)]).

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

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

fof(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(d7_euclid,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k14_euclid(A) = g1_metric_1(k1_euclid(A),k13_euclid(A)) ) ),
    file(euclid,d7_euclid),
    [interesting(0.9),axiom,file(euclid,d7_euclid)]).

fof(commutativity_k17_euclid,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => k17_euclid(A,B,C) = k17_euclid(A,C,B) ) ),
    file(euclid,k17_euclid),
    [interesting(0.9),axiom,file(euclid,k17_euclid)]).

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

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

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

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

fof(dt_k15_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & l1_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,k15_euclid),
    [interesting(0.9),axiom,file(euclid,k15_euclid)]).

fof(dt_k17_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k17_euclid(A,B,C),u1_struct_0(k15_euclid(A))) ) ),
    file(euclid,k17_euclid),
    [interesting(0.9),axiom,file(euclid,k17_euclid)]).

fof(dt_k19_euclid,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k19_euclid(A,B),u1_struct_0(k15_euclid(A))) ) ),
    file(euclid,k19_euclid),
    [interesting(0.9),axiom,file(euclid,k19_euclid)]).

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

fof(dt_k20_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k20_euclid(A,B,C),u1_struct_0(k15_euclid(A))) ) ),
    file(euclid,k20_euclid),
    [interesting(0.9),axiom,file(euclid,k20_euclid)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

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

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(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_7__jordan2c,assumption,(
    m2_subset_1(c1_7__jordan2c,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(jordan2c,c1_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c1_7__jordan2c)]).

fof(dt_c2_7__jordan2c,assumption,(
    m1_subset_1(c2_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c))) ),
    introduced(assumption,[file(jordan2c,c2_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c2_7__jordan2c)]).

fof(dt_c3_7__jordan2c,assumption,(
    m1_subset_1(c3_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c))) ),
    introduced(assumption,[file(jordan2c,c3_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c3_7__jordan2c)]).

fof(dt_c4_7__jordan2c,assumption,(
    m1_subset_1(c4_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c))) ),
    introduced(assumption,[file(jordan2c,c4_7__jordan2c)]),
    [interesting(0.8),axiom,file(jordan2c,c4_7__jordan2c)]).

fof(fc2_euclid,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,fc2_euclid),
    [interesting(0.9),axiom,file(euclid,fc2_euclid)]).

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(fc2_topreal1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & v3_compts_1(k15_euclid(A)) ) ) ),
    file(topreal1,fc2_topreal1),
    [interesting(0.9),axiom,file(topreal1,fc2_topreal1)]).

fof(d8_euclid,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k15_euclid(A) = k5_pcomps_1(k14_euclid(A)) ) ),
    file(euclid,d8_euclid),
    [interesting(0.9),axiom,file(euclid,d8_euclid)]).

fof(t45_euclid,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => k20_euclid(A,B,C) = k17_euclid(A,B,k19_euclid(A,C)) ) ) ) ),
    file(euclid,t45_euclid),
    [interesting(0.9),axiom,file(euclid,t45_euclid)]).

fof(e1_7_1__jordan2c,plain,(
    k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),c4_7__jordan2c) = k17_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),k19_euclid(c1_7__jordan2c,c4_7__jordan2c)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c])],[existence_m1_finseq_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_k4_finseq_2,dt_m1_finseq_2,dt_m1_relset_1,dt_m2_relset_1,dt_u1_metric_1,cc1_finseq_1,cc1_relset_1,cc2_funct_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc1_finseq_1,rc1_funct_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_tbsp_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_tbsp_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,free_g1_metric_1,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,abstractness_v1_metric_1,existence_l1_metric_1,dt_g1_metric_1,dt_g1_pre_topc,dt_k13_euclid,dt_k1_euclid,dt_k1_xboole_0,dt_l1_metric_1,dt_u1_pre_topc,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_tbsp_1,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc3_pcomps_1,fc4_pcomps_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_metric_1,rc1_xreal_0,rc2_metric_1,rc3_finset_1,rc3_metric_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_euclid,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k14_euclid,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_pcomps_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_euclid,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_pre_topc,rc1_subset_1,rc2_pcomps_1,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d7_euclid,commutativity_k17_euclid,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k17_euclid,dt_k19_euclid,dt_k1_numbers,dt_k20_euclid,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c,fc2_euclid,fc2_membered,fc2_topreal1,d8_euclid,t45_euclid]),
    [interesting(0.65),file(jordan2c,e1_7_1__jordan2c),[file(jordan2c,e1_7_1__jordan2c)]]).

fof(t30_euclid,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => k17_euclid(A,k17_euclid(A,B,C),D) = k17_euclid(A,B,k17_euclid(A,C,D)) ) ) ) ) ),
    file(euclid,t30_euclid),
    [interesting(0.9),axiom,file(euclid,t30_euclid)]).

fof(e2_7_1__jordan2c,plain,(
    k17_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),k19_euclid(c1_7__jordan2c,c4_7__jordan2c)) = k17_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,k19_euclid(c1_7__jordan2c,c4_7__jordan2c)),c3_7__jordan2c) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c])],[existence_m1_finseq_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_k4_finseq_2,dt_m1_finseq_2,dt_m1_relset_1,dt_m2_relset_1,dt_u1_metric_1,cc1_finseq_1,cc1_relset_1,cc2_funct_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc1_finseq_1,rc1_funct_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_tbsp_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_tbsp_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,free_g1_metric_1,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,abstractness_v1_metric_1,existence_l1_metric_1,dt_g1_metric_1,dt_g1_pre_topc,dt_k13_euclid,dt_k1_euclid,dt_k1_xboole_0,dt_l1_metric_1,dt_u1_pre_topc,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_tbsp_1,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc3_pcomps_1,fc4_pcomps_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_metric_1,rc1_xreal_0,rc2_metric_1,rc3_finset_1,rc3_metric_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_euclid,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k14_euclid,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_pcomps_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_euclid,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_pre_topc,rc1_subset_1,rc2_pcomps_1,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d7_euclid,commutativity_k17_euclid,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k17_euclid,dt_k19_euclid,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c,fc2_euclid,fc2_membered,fc2_topreal1,d8_euclid,t30_euclid]),
    [interesting(0.65),file(jordan2c,e2_7_1__jordan2c),[file(jordan2c,e2_7_1__jordan2c)]]).

fof(e3_7_1__jordan2c,plain,(
    k17_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,k19_euclid(c1_7__jordan2c,c4_7__jordan2c)),c3_7__jordan2c) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,c4_7__jordan2c),c3_7__jordan2c) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c])],[existence_m1_finseq_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_k4_finseq_2,dt_m1_finseq_2,dt_m1_relset_1,dt_m2_relset_1,dt_u1_metric_1,cc1_finseq_1,cc1_relset_1,cc2_funct_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc1_finseq_1,rc1_funct_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_tbsp_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_tbsp_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,free_g1_metric_1,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,abstractness_v1_metric_1,existence_l1_metric_1,dt_g1_metric_1,dt_g1_pre_topc,dt_k13_euclid,dt_k1_euclid,dt_k1_xboole_0,dt_l1_metric_1,dt_u1_pre_topc,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_tbsp_1,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc3_pcomps_1,fc4_pcomps_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_metric_1,rc1_xreal_0,rc2_metric_1,rc3_finset_1,rc3_metric_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_euclid,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k14_euclid,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k5_pcomps_1,dt_l1_pre_topc,dt_l1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_euclid,fc1_struct_0,fc1_subset_1,fc5_membered,rc1_pre_topc,rc1_subset_1,rc2_pcomps_1,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d7_euclid,commutativity_k17_euclid,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k17_euclid,dt_k19_euclid,dt_k1_numbers,dt_k20_euclid,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c,fc2_euclid,fc2_membered,fc2_topreal1,d8_euclid,t45_euclid]),
    [interesting(0.65),file(jordan2c,e3_7_1__jordan2c),[file(jordan2c,e3_7_1__jordan2c)]]).

fof(e1_7__jordan2c,plain,(
    k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),c4_7__jordan2c) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,c4_7__jordan2c),c3_7__jordan2c) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c])],[e1_7_1__jordan2c,e2_7_1__jordan2c,e3_7_1__jordan2c]),
    [interesting(0.8),file(jordan2c,e1_7__jordan2c),[file(jordan2c,e1_7__jordan2c)]]).

fof(i5_7__jordan2c,theorem,(
    $true ),
    introduced(tautology,[file(jordan2c,i5_7__jordan2c)]),
    [interesting(0.8),trivial,file(jordan2c,i5_7__jordan2c)]).

fof(i4_7__jordan2c,plain,(
    k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),c4_7__jordan2c) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,c4_7__jordan2c),c3_7__jordan2c) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c,dt_c4_7__jordan2c])],[e1_7__jordan2c,i5_7__jordan2c]),
    [interesting(0.8),file(jordan2c,i4_7__jordan2c),[file(jordan2c,i4_7__jordan2c)]]).

fof(i4_7_tmp__jordan2c,plain,
    ( m1_subset_1(c4_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c)))
   => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),c4_7__jordan2c) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,c4_7__jordan2c),c3_7__jordan2c) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c]),discharge_asm(discharge,[dt_c4_7__jordan2c])],[dt_c4_7__jordan2c,i4_7__jordan2c]),
    [interesting(0.8),i3_7__jordan2c]).

fof(i3_7__jordan2c,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
     => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),A) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,A),c3_7__jordan2c) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c,dt_c3_7__jordan2c])],[i4_7_tmp__jordan2c,dh_c4_7__jordan2c]),
    [interesting(0.8),file(jordan2c,i3_7__jordan2c),[file(jordan2c,i3_7__jordan2c)]]).

fof(i3_7_tmp__jordan2c,plain,
    ( m1_subset_1(c3_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c)))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
       => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,c3_7__jordan2c),A) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,A),c3_7__jordan2c) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c]),discharge_asm(discharge,[dt_c3_7__jordan2c])],[dt_c3_7__jordan2c,i3_7__jordan2c]),
    [interesting(0.8),i2_7__jordan2c]).

fof(i2_7__jordan2c,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
         => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,A),B) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,B),A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__jordan2c,dt_c2_7__jordan2c])],[i3_7_tmp__jordan2c,dh_c3_7__jordan2c]),
    [interesting(0.8),file(jordan2c,i2_7__jordan2c),[file(jordan2c,i2_7__jordan2c)]]).

fof(i2_7_tmp__jordan2c,plain,
    ( m1_subset_1(c2_7__jordan2c,u1_struct_0(k15_euclid(c1_7__jordan2c)))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
           => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,c2_7__jordan2c,A),B) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,c2_7__jordan2c,B),A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__jordan2c]),discharge_asm(discharge,[dt_c2_7__jordan2c])],[dt_c2_7__jordan2c,i2_7__jordan2c]),
    [interesting(0.8),i1_7__jordan2c]).

fof(i1_7__jordan2c,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(c1_7__jordan2c)))
             => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,A,B),C) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,A,C),B) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__jordan2c])],[i2_7_tmp__jordan2c,dh_c2_7__jordan2c]),
    [interesting(0.8),file(jordan2c,i1_7__jordan2c),[file(jordan2c,i1_7__jordan2c)]]).

fof(i1_7_tmp__jordan2c,plain,
    ( m2_subset_1(c1_7__jordan2c,k1_numbers,k5_numbers)
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_7__jordan2c)))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(k15_euclid(c1_7__jordan2c)))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(k15_euclid(c1_7__jordan2c)))
               => k20_euclid(c1_7__jordan2c,k17_euclid(c1_7__jordan2c,A,B),C) = k17_euclid(c1_7__jordan2c,k20_euclid(c1_7__jordan2c,A,C),B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__jordan2c])],[dt_c1_7__jordan2c,i1_7__jordan2c]),
    [interesting(1),t9_jordan2c]).

fof(t9_jordan2c,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => k20_euclid(A,k17_euclid(A,B,C),D) = k17_euclid(A,k20_euclid(A,B,D),C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__jordan2c,dh_c1_7__jordan2c]),
    [interesting(1),file(jordan2c,t9_jordan2c),[file(jordan2c,t9_jordan2c)]]).