% Mizar ND problem: t5_group_4,group_4,183,20 
fof(dh_c1_7__group_4,definition,
    ( ( m2_subset_1(c1_7__group_4,k1_numbers,k5_numbers)
     => ! [A] : 
          ( ( ~ v3_struct_0(A)
            & v3_group_1(A)
            & v4_group_1(A)
            & l1_group_1(A) )
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_group_2(C,A)
                 => ( r1_rlvect_1(C,B)
                   => r1_rlvect_1(C,k6_group_1(A,c1_7__group_4,B)) ) ) ) ) )
   => ! [D] : 
        ( m2_subset_1(D,k1_numbers,k5_numbers)
       => ! [E] : 
            ( ( ~ v3_struct_0(E)
              & v3_group_1(E)
              & v4_group_1(E)
              & l1_group_1(E) )
           => ! [F] : 
                ( m1_subset_1(F,u1_struct_0(E))
               => ! [G] : 
                    ( m1_group_2(G,E)
                   => ( r1_rlvect_1(G,F)
                     => r1_rlvect_1(G,k6_group_1(E,D,F)) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_7__group_4),file(group_4,c1_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c1_7__group_4)]).

fof(dh_c2_7__group_4,definition,
    ( ( ( ~ v3_struct_0(c2_7__group_4)
        & v3_group_1(c2_7__group_4)
        & v4_group_1(c2_7__group_4)
        & l1_group_1(c2_7__group_4) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c2_7__group_4))
         => ! [B] : 
              ( m1_group_2(B,c2_7__group_4)
             => ( r1_rlvect_1(B,A)
               => r1_rlvect_1(B,k6_group_1(c2_7__group_4,c1_7__group_4,A)) ) ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & v3_group_1(C)
          & v4_group_1(C)
          & l1_group_1(C) )
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(C))
           => ! [E] : 
                ( m1_group_2(E,C)
               => ( r1_rlvect_1(E,D)
                 => r1_rlvect_1(E,k6_group_1(C,c1_7__group_4,D)) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_7__group_4),file(group_4,c2_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c2_7__group_4)]).

fof(dh_c3_7__group_4,definition,
    ( ( m1_subset_1(c3_7__group_4,u1_struct_0(c2_7__group_4))
     => ! [A] : 
          ( m1_group_2(A,c2_7__group_4)
         => ( r1_rlvect_1(A,c3_7__group_4)
           => r1_rlvect_1(A,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c2_7__group_4))
       => ! [C] : 
            ( m1_group_2(C,c2_7__group_4)
           => ( r1_rlvect_1(C,B)
             => r1_rlvect_1(C,k6_group_1(c2_7__group_4,c1_7__group_4,B)) ) ) ) ),
    introduced(definition,[new_symbol(c3_7__group_4),file(group_4,c3_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c3_7__group_4)]).

fof(dh_c4_7__group_4,definition,
    ( ( m1_group_2(c4_7__group_4,c2_7__group_4)
     => ( r1_rlvect_1(c4_7__group_4,c3_7__group_4)
       => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ) )
   => ! [A] : 
        ( m1_group_2(A,c2_7__group_4)
       => ( r1_rlvect_1(A,c3_7__group_4)
         => r1_rlvect_1(A,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ) ) ),
    introduced(definition,[new_symbol(c4_7__group_4),file(group_4,c4_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c4_7__group_4)]).

fof(e1_7__group_4,assumption,(
    r1_rlvect_1(c4_7__group_4,c3_7__group_4) ),
    introduced(assumption,[file(group_4,e1_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,e1_7__group_4)]).

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(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(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(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(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_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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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

fof(cc3_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    [interesting(0.9),axiom,file(int_1,cc3_int_1)]).

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

fof(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(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(rc1_int_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v1_int_1(A) ) ),
    file(int_1,rc1_int_1),
    [interesting(0.9),axiom,file(int_1,rc1_int_1)]).

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

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

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

fof(rc3_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(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(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    [interesting(0.9),axiom,file(group_1,l1_group_1)]).

fof(existence_m1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ? [B] : m1_group_2(B,A) ) ),
    file(group_2,m1_group_2),
    [interesting(0.9),axiom,file(group_2,m1_group_2)]).

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

fof(dt_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_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    [interesting(0.9),axiom,file(group_1,l1_group_1)]).

fof(dt_m1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) ) ) ) ),
    file(group_2,m1_group_2),
    [interesting(0.9),axiom,file(group_2,m1_group_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(cc1_group_1,theorem,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(group_1,cc1_group_1),
    [interesting(0.9),axiom,file(group_1,cc1_group_1)]).

fof(cc1_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => v4_group_1(B) ) ) ),
    file(group_2,cc1_group_2),
    [interesting(0.9),axiom,file(group_2,cc1_group_2)]).

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

fof(cc2_int_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_int_1(A) ) ) ),
    file(int_1,cc2_int_1),
    [interesting(0.9),axiom,file(int_1,cc2_int_1)]).

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

fof(cc4_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    [interesting(0.9),axiom,file(int_1,cc4_int_1)]).

fof(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(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_int_1,theorem,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    [interesting(0.9),axiom,file(int_1,rc2_int_1)]).

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

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

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

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

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

fof(dt_k6_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_int_1(B)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k6_group_1),
    [interesting(0.9),axiom,file(group_1,k6_group_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_c1_7__group_4,assumption,(
    m2_subset_1(c1_7__group_4,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(group_4,c1_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c1_7__group_4)]).

fof(dt_c2_7__group_4,assumption,
    ( ~ v3_struct_0(c2_7__group_4)
    & v3_group_1(c2_7__group_4)
    & v4_group_1(c2_7__group_4)
    & l1_group_1(c2_7__group_4) ),
    introduced(assumption,[file(group_4,c2_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c2_7__group_4)]).

fof(dt_c3_7__group_4,assumption,(
    m1_subset_1(c3_7__group_4,u1_struct_0(c2_7__group_4)) ),
    introduced(assumption,[file(group_4,c3_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c3_7__group_4)]).

fof(dt_c4_7__group_4,assumption,(
    m1_group_2(c4_7__group_4,c2_7__group_4) ),
    introduced(assumption,[file(group_4,c4_7__group_4)]),
    [interesting(0.8),axiom,file(group_4,c4_7__group_4)]).

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

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

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

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

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

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

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

fof(fc6_int_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & v1_int_1(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v1_int_1(k2_xcmplx_0(B,A)) ) ) ),
    file(int_1,fc6_int_1),
    [interesting(0.9),axiom,file(int_1,fc6_int_1)]).

fof(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(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(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(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

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

fof(s1_nat_1__e5_7__group_4,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_group_2(C,A) )
     => ( ( r1_rlvect_1(C,k6_group_1(A,0,B))
          & ! [D] : 
              ( m2_subset_1(D,k1_numbers,k5_numbers)
             => ( r1_rlvect_1(C,k6_group_1(A,D,B))
               => r1_rlvect_1(C,k6_group_1(A,k1_nat_1(D,1),B)) ) ) )
       => ! [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
           => r1_rlvect_1(C,k6_group_1(A,D,B)) ) ) ) ),
    file(group_4,s1_nat_1__e5_7__group_4),
    [interesting(0.9),axiom,file(group_4,s1_nat_1__e5_7__group_4)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(dt_k2_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ),
    file(group_1,k2_group_1),
    [interesting(0.9),axiom,file(group_1,k2_group_1)]).

fof(t43_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_group_1(A,0,B) = k2_group_1(A) ) ) ),
    file(group_1,t43_group_1),
    [interesting(0.9),axiom,file(group_1,t43_group_1)]).

fof(e2_7__group_4,plain,(
    k6_group_1(c2_7__group_4,0,c3_7__group_4) = k2_group_1(c2_7__group_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_7__group_4,dt_c3_7__group_4])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_int_1,cc3_nat_1,fc1_subset_1,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc1_subset_1,rc2_nat_1,rc2_subset_1,rc3_nat_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,cc1_nat_1,cc2_int_1,cc2_nat_1,cc4_int_1,fc1_numbers,fc1_struct_0,rc2_int_1,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_m1_subset_1,dt_k2_group_1,dt_k6_group_1,dt_l1_group_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_7__group_4,dt_c3_7__group_4,cc1_group_1,spc0_numerals,spc0_boole,t43_group_1]),
    [interesting(0.8),file(group_4,e2_7__group_4),[file(group_4,e2_7__group_4)]]).

fof(t55_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => r1_rlvect_1(B,k2_group_1(A)) ) ) ),
    file(group_2,t55_group_2),
    [interesting(0.9),axiom,file(group_2,t55_group_2)]).

fof(e3_7__group_4,plain,(
    r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,0,c3_7__group_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_int_1,cc3_nat_1,fc1_subset_1,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc1_subset_1,rc2_nat_1,rc2_subset_1,rc3_nat_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc1_nat_1,cc2_int_1,cc2_nat_1,cc4_int_1,fc1_numbers,fc1_struct_0,rc2_int_1,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_m1_group_2,dt_k2_group_1,dt_k6_group_1,dt_l1_group_1,dt_m1_group_2,dt_c2_7__group_4,dt_c3_7__group_4,dt_c4_7__group_4,cc1_group_1,cc1_group_2,spc0_numerals,spc0_boole,e2_7__group_4,t55_group_2]),
    [interesting(0.8),file(group_4,e3_7__group_4),[file(group_4,e3_7__group_4)]]).

fof(dh_c1_7_1__group_4,definition,
    ( ( m2_subset_1(c1_7_1__group_4,k1_numbers,k5_numbers)
     => ( r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7_1__group_4,c3_7__group_4))
       => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(c1_7_1__group_4,1),c3_7__group_4)) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,A,c3_7__group_4))
         => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(A,1),c3_7__group_4)) ) ) ),
    introduced(definition,[new_symbol(c1_7_1__group_4),file(group_4,c1_7_1__group_4)]),
    [interesting(0.65),axiom,file(group_4,c1_7_1__group_4)]).

fof(e1_7_1__group_4,assumption,(
    r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7_1__group_4,c3_7__group_4)) ),
    introduced(assumption,[file(group_4,e1_7_1__group_4)]),
    [interesting(0.65),axiom,file(group_4,e1_7_1__group_4)]).

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(dt_k1_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k1_group_1),
    [interesting(0.9),axiom,file(group_1,k1_group_1)]).

fof(dt_c1_7_1__group_4,assumption,(
    m2_subset_1(c1_7_1__group_4,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(group_4,c1_7_1__group_4)]),
    [interesting(0.65),axiom,file(group_4,c1_7_1__group_4)]).

fof(t49_group_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ( k6_group_1(B,k1_nat_1(A,1),C) = k1_group_1(B,k6_group_1(B,A,C),C)
                & k6_group_1(B,k1_nat_1(A,1),C) = k1_group_1(B,C,k6_group_1(B,A,C)) ) ) ) ) ),
    file(group_1,t49_group_1),
    [interesting(0.9),axiom,file(group_1,t49_group_1)]).

fof(e2_7_1__group_4,plain,(
    k6_group_1(c2_7__group_4,k1_nat_1(c1_7_1__group_4,1),c3_7__group_4) = k1_group_1(c2_7__group_4,k6_group_1(c2_7__group_4,c1_7_1__group_4,c3_7__group_4),c3_7__group_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7_1__group_4,dt_c2_7__group_4,dt_c3_7__group_4])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_l1_struct_0,cc3_int_1,cc3_nat_1,cc4_int_1,fc1_int_1,fc1_nat_1,fc1_struct_0,fc1_subset_1,fc3_nat_1,fc4_nat_1,fc6_int_1,rc1_int_1,rc1_nat_1,rc1_subset_1,rc2_int_1,rc2_nat_1,rc2_subset_1,rc3_nat_1,rc3_struct_0,rc5_struct_0,spc6_arithm,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_l1_group_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_group_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_numbers,dt_k6_group_1,dt_l1_group_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_7_1__group_4,dt_c2_7__group_4,dt_c3_7__group_4,cc1_group_1,cc1_nat_1,cc2_int_1,cc2_nat_1,fc1_numbers,spc1_numerals,spc1_boole,t49_group_1]),
    [interesting(0.65),file(group_4,e2_7_1__group_4),[file(group_4,e2_7_1__group_4)]]).

fof(t59_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k1_group_1(A,B,C)) ) ) ) ) ) ),
    file(group_2,t59_group_2),
    [interesting(0.9),axiom,file(group_2,t59_group_2)]).

fof(e3_7_1__group_4,plain,(
    r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(c1_7_1__group_4,1),c3_7__group_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_7__group_4,dt_c1_7_1__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4,e1_7_1__group_4])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_int_1,cc3_nat_1,fc1_nat_1,fc1_subset_1,fc2_finseq_1,fc3_nat_1,fc4_nat_1,rc1_int_1,rc1_nat_1,rc1_subset_1,rc2_nat_1,rc2_subset_1,rc3_nat_1,rc5_struct_0,spc6_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_l1_struct_0,dt_m2_subset_1,cc1_nat_1,cc2_int_1,cc2_nat_1,cc4_int_1,fc1_int_1,fc1_numbers,fc1_struct_0,fc6_int_1,rc2_int_1,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,redefinition_k1_nat_1,dt_k1_group_1,dt_k1_nat_1,dt_k6_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7_1__group_4,dt_c2_7__group_4,dt_c3_7__group_4,dt_c4_7__group_4,cc1_group_1,cc1_group_2,spc1_numerals,spc1_boole,e2_7_1__group_4,e1_7__group_4,e1_7_1__group_4,t59_group_2]),
    [interesting(0.65),file(group_4,e3_7_1__group_4),[file(group_4,e3_7_1__group_4)]]).

fof(i3_7_1__group_4,theorem,(
    $true ),
    introduced(tautology,[file(group_4,i3_7_1__group_4)]),
    [interesting(0.65),trivial,file(group_4,i3_7_1__group_4)]).

fof(i2_7_1__group_4,plain,(
    r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(c1_7_1__group_4,1),c3_7__group_4)) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_7__group_4,dt_c1_7_1__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4,e1_7_1__group_4])],[e3_7_1__group_4,i3_7_1__group_4]),
    [interesting(0.65),file(group_4,i2_7_1__group_4),[file(group_4,i2_7_1__group_4)]]).

fof(i1_7_1__group_4,plain,
    ( r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7_1__group_4,c3_7__group_4))
   => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(c1_7_1__group_4,1),c3_7__group_4)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_7__group_4,dt_c1_7_1__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4]),discharge_asm(discharge,[e1_7_1__group_4])],[e1_7_1__group_4,i2_7_1__group_4]),
    [interesting(0.65),file(group_4,i1_7_1__group_4),[file(group_4,i1_7_1__group_4)]]).

fof(i1_7_1_tmp__group_4,plain,
    ( m2_subset_1(c1_7_1__group_4,k1_numbers,k5_numbers)
   => ( r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7_1__group_4,c3_7__group_4))
     => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(c1_7_1__group_4,1),c3_7__group_4)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4]),discharge_asm(discharge,[dt_c1_7_1__group_4])],[dt_c1_7_1__group_4,i1_7_1__group_4]),
    [interesting(0.8),e4_7__group_4]).

fof(e4_7__group_4,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,A,c3_7__group_4))
       => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,k1_nat_1(A,1),c3_7__group_4)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4])],[i1_7_1_tmp__group_4,dh_c1_7_1__group_4]),
    [interesting(0.8),file(group_4,e4_7__group_4),[file(group_4,e4_7__group_4)]]).

fof(e5_7__group_4,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,A,c3_7__group_4)) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4])],[commutativity_k2_xcmplx_0,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_l1_struct_0,cc3_int_1,cc3_nat_1,cc4_int_1,fc1_int_1,fc1_nat_1,fc1_struct_0,fc1_subset_1,fc3_nat_1,fc4_nat_1,fc6_int_1,rc1_int_1,rc1_nat_1,rc1_subset_1,rc2_int_1,rc2_nat_1,rc2_subset_1,rc3_nat_1,rc3_struct_0,rc5_struct_0,commutativity_k1_nat_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k5_numbers,dt_k6_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c2_7__group_4,dt_c3_7__group_4,dt_c4_7__group_4,cc1_group_1,cc1_group_2,cc1_nat_1,cc2_int_1,cc2_nat_1,fc1_numbers,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,s1_nat_1__e5_7__group_4,e3_7__group_4,e4_7__group_4]),
    [interesting(0.8),file(group_4,e5_7__group_4),[file(group_4,e5_7__group_4)]]).

fof(e6_7__group_4,plain,(
    r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_4,dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,dt_k1_xboole_0,dt_l1_struct_0,cc3_int_1,cc3_nat_1,fc1_struct_0,fc2_finseq_1,rc1_int_1,rc1_nat_1,rc2_nat_1,rc3_nat_1,rc3_struct_0,rc5_struct_0,t1_subset,t4_subset,t5_subset,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,cc1_nat_1,cc2_int_1,cc2_nat_1,cc4_int_1,fc1_subset_1,rc1_subset_1,rc2_int_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_k6_group_1,dt_m2_subset_1,dt_c1_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4,dt_c4_7__group_4,fc1_numbers,e5_7__group_4]),
    [interesting(0.8),file(group_4,e6_7__group_4),[file(group_4,e6_7__group_4)]]).

fof(i6_7__group_4,theorem,(
    $true ),
    introduced(tautology,[file(group_4,i6_7__group_4)]),
    [interesting(0.8),trivial,file(group_4,i6_7__group_4)]).

fof(i5_7__group_4,plain,(
    r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__group_4,dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4,e1_7__group_4])],[e6_7__group_4,i6_7__group_4]),
    [interesting(0.8),file(group_4,i5_7__group_4),[file(group_4,i5_7__group_4)]]).

fof(i4_7__group_4,plain,
    ( r1_rlvect_1(c4_7__group_4,c3_7__group_4)
   => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__group_4,dt_c4_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4]),discharge_asm(discharge,[e1_7__group_4])],[e1_7__group_4,i5_7__group_4]),
    [interesting(0.8),file(group_4,i4_7__group_4),[file(group_4,i4_7__group_4)]]).

fof(i4_7_tmp__group_4,plain,
    ( m1_group_2(c4_7__group_4,c2_7__group_4)
   => ( r1_rlvect_1(c4_7__group_4,c3_7__group_4)
     => r1_rlvect_1(c4_7__group_4,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4]),discharge_asm(discharge,[dt_c4_7__group_4])],[dt_c4_7__group_4,i4_7__group_4]),
    [interesting(0.8),i3_7__group_4]).

fof(i3_7__group_4,plain,(
    ! [A] : 
      ( m1_group_2(A,c2_7__group_4)
     => ( r1_rlvect_1(A,c3_7__group_4)
       => r1_rlvect_1(A,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__group_4,dt_c2_7__group_4,dt_c3_7__group_4])],[i4_7_tmp__group_4,dh_c4_7__group_4]),
    [interesting(0.8),file(group_4,i3_7__group_4),[file(group_4,i3_7__group_4)]]).

fof(i3_7_tmp__group_4,plain,
    ( m1_subset_1(c3_7__group_4,u1_struct_0(c2_7__group_4))
   => ! [A] : 
        ( m1_group_2(A,c2_7__group_4)
       => ( r1_rlvect_1(A,c3_7__group_4)
         => r1_rlvect_1(A,k6_group_1(c2_7__group_4,c1_7__group_4,c3_7__group_4)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__group_4,dt_c2_7__group_4]),discharge_asm(discharge,[dt_c3_7__group_4])],[dt_c3_7__group_4,i3_7__group_4]),
    [interesting(0.8),i2_7__group_4]).

fof(i2_7__group_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c2_7__group_4))
     => ! [B] : 
          ( m1_group_2(B,c2_7__group_4)
         => ( r1_rlvect_1(B,A)
           => r1_rlvect_1(B,k6_group_1(c2_7__group_4,c1_7__group_4,A)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__group_4,dt_c2_7__group_4])],[i3_7_tmp__group_4,dh_c3_7__group_4]),
    [interesting(0.8),file(group_4,i2_7__group_4),[file(group_4,i2_7__group_4)]]).

fof(i2_7_tmp__group_4,plain,
    ( ( ~ v3_struct_0(c2_7__group_4)
      & v3_group_1(c2_7__group_4)
      & v4_group_1(c2_7__group_4)
      & l1_group_1(c2_7__group_4) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c2_7__group_4))
       => ! [B] : 
            ( m1_group_2(B,c2_7__group_4)
           => ( r1_rlvect_1(B,A)
             => r1_rlvect_1(B,k6_group_1(c2_7__group_4,c1_7__group_4,A)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__group_4]),discharge_asm(discharge,[dt_c2_7__group_4])],[dt_c2_7__group_4,i2_7__group_4]),
    [interesting(0.8),i1_7__group_4]).

fof(i1_7__group_4,plain,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_group_2(C,A)
             => ( r1_rlvect_1(C,B)
               => r1_rlvect_1(C,k6_group_1(A,c1_7__group_4,B)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__group_4])],[i2_7_tmp__group_4,dh_c2_7__group_4]),
    [interesting(0.8),file(group_4,i1_7__group_4),[file(group_4,i1_7__group_4)]]).

fof(i1_7_tmp__group_4,plain,
    ( m2_subset_1(c1_7__group_4,k1_numbers,k5_numbers)
   => ! [A] : 
        ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & l1_group_1(A) )
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_group_2(C,A)
               => ( r1_rlvect_1(C,B)
                 => r1_rlvect_1(C,k6_group_1(A,c1_7__group_4,B)) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__group_4])],[dt_c1_7__group_4,i1_7__group_4]),
    [interesting(1),t5_group_4]).

fof(t5_group_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_group_2(D,B)
                 => ( r1_rlvect_1(D,C)
                   => r1_rlvect_1(D,k6_group_1(B,A,C)) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__group_4,dh_c1_7__group_4]),
    [interesting(1),file(group_4,t5_group_4),[file(group_4,t5_group_4)]]).