% Mizar ND problem: t4_group_3,group_3,87,37 
fof(dh_c1_4__group_3,definition,
    ( ( ( ~ v3_struct_0(c1_4__group_3)
        & v3_group_1(c1_4__group_3)
        & v4_group_1(c1_4__group_3)
        & l1_group_1(c1_4__group_3) )
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
                     => ( ( r1_tarski(A,B)
                          & r1_tarski(C,D) )
                       => r1_tarski(k2_group_2(c1_4__group_3,A,C),k2_group_2(c1_4__group_3,B,D)) ) ) ) ) ) )
   => ! [E] : 
        ( ( ~ v3_struct_0(E)
          & v3_group_1(E)
          & v4_group_1(E)
          & l1_group_1(E) )
       => ! [F] : 
            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(E)))
           => ! [G] : 
                ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(E)))
               => ! [H] : 
                    ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(E)))
                   => ! [I] : 
                        ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(E)))
                       => ( ( r1_tarski(F,G)
                            & r1_tarski(H,I) )
                         => r1_tarski(k2_group_2(E,F,H),k2_group_2(E,G,I)) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__group_3),file(group_3,c1_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c1_4__group_3)]).

fof(dh_c2_4__group_3,definition,
    ( ( m1_subset_1(c2_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
                 => ( ( r1_tarski(c2_4__group_3,A)
                      & r1_tarski(B,C) )
                   => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,B),k2_group_2(c1_4__group_3,A,C)) ) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ! [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
           => ! [F] : 
                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
               => ! [G] : 
                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
                   => ( ( r1_tarski(D,E)
                        & r1_tarski(F,G) )
                     => r1_tarski(k2_group_2(c1_4__group_3,D,F),k2_group_2(c1_4__group_3,E,G)) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__group_3),file(group_3,c2_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c2_4__group_3)]).

fof(dh_c3_4__group_3,definition,
    ( ( m1_subset_1(c3_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
             => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
                  & r1_tarski(A,B) )
               => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,A),k2_group_2(c1_4__group_3,c3_4__group_3,B)) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
           => ! [E] : 
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
               => ( ( r1_tarski(c2_4__group_3,C)
                    & r1_tarski(D,E) )
                 => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,D),k2_group_2(c1_4__group_3,C,E)) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_4__group_3),file(group_3,c3_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c3_4__group_3)]).

fof(dh_c4_4__group_3,definition,
    ( ( m1_subset_1(c4_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
              & r1_tarski(c4_4__group_3,A) )
           => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,A)) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
           => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
                & r1_tarski(B,C) )
             => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,B),k2_group_2(c1_4__group_3,c3_4__group_3,C)) ) ) ) ),
    introduced(definition,[new_symbol(c4_4__group_3),file(group_3,c4_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c4_4__group_3)]).

fof(dh_c5_4__group_3,definition,
    ( ( m1_subset_1(c5_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
          & r1_tarski(c4_4__group_3,c5_4__group_3) )
       => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
            & r1_tarski(c4_4__group_3,A) )
         => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,A)) ) ) ),
    introduced(definition,[new_symbol(c5_4__group_3),file(group_3,c5_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c5_4__group_3)]).

fof(e1_4__group_3,assumption,
    ( r1_tarski(c2_4__group_3,c3_4__group_3)
    & r1_tarski(c4_4__group_3,c5_4__group_3) ),
    introduced(assumption,[file(group_3,e1_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,e1_4__group_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(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(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(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(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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(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(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_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_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(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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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

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

fof(dt_k2_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k2_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k2_group_2),
    [interesting(0.9),axiom,file(group_2,k2_group_2)]).

fof(dt_c1_4__group_3,assumption,
    ( ~ v3_struct_0(c1_4__group_3)
    & v3_group_1(c1_4__group_3)
    & v4_group_1(c1_4__group_3)
    & l1_group_1(c1_4__group_3) ),
    introduced(assumption,[file(group_3,c1_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c1_4__group_3)]).

fof(dt_c2_4__group_3,assumption,(
    m1_subset_1(c2_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3))) ),
    introduced(assumption,[file(group_3,c2_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c2_4__group_3)]).

fof(dt_c3_4__group_3,assumption,(
    m1_subset_1(c3_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3))) ),
    introduced(assumption,[file(group_3,c3_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c3_4__group_3)]).

fof(dt_c4_4__group_3,assumption,(
    m1_subset_1(c4_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3))) ),
    introduced(assumption,[file(group_3,c4_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c4_4__group_3)]).

fof(dt_c5_4__group_3,assumption,(
    m1_subset_1(c5_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3))) ),
    introduced(assumption,[file(group_3,c5_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c5_4__group_3)]).

fof(dt_c6_4__group_3,assumption,(
    $true ),
    introduced(assumption,[file(group_3,c6_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c6_4__group_3)]).

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_c6_4__group_3,definition,
    ( ~ ( r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3))
        & ~ r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3))
          & ~ r2_hidden(A,k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ) ),
    introduced(definition,[new_symbol(c6_4__group_3),file(group_3,c6_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c6_4__group_3)]).

fof(e2_4__group_3,assumption,(
    r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3)) ),
    introduced(assumption,[file(group_3,e2_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,e2_4__group_3)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc2_finset_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_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(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

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(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_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(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

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_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_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    [interesting(0.9),axiom,file(binop_1,k1_binop_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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

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(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(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(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(d1_binop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    [interesting(0.9),axiom,file(binop_1,d1_binop_1)]).

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_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_k2_binop_1,definition,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    [interesting(0.9),axiom,file(binop_1,k2_binop_1)]).

fof(dt_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    [interesting(0.9),axiom,file(binop_1,k2_binop_1)]).

fof(dt_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    [interesting(0.9),axiom,file(group_1,u1_group_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(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(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(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(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_3_0_group_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_group_2(B,C,D))
      <=> ? [E,F] : 
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k1_group_1(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) ),
    file(group_2,a_3_0_group_2),
    [interesting(0.9),axiom,file(group_2,a_3_0_group_2)]).

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(dh_c7_4__group_3,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_4__group_3))
        & ? [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_4__group_3))
            & c6_4__group_3 = k1_group_1(c1_4__group_3,A,B)
            & r2_hidden(A,c2_4__group_3)
            & r2_hidden(B,c4_4__group_3) ) )
   => ( m1_subset_1(c7_4__group_3,u1_struct_0(c1_4__group_3))
      & ? [C] : 
          ( m1_subset_1(C,u1_struct_0(c1_4__group_3))
          & c6_4__group_3 = k1_group_1(c1_4__group_3,c7_4__group_3,C)
          & r2_hidden(c7_4__group_3,c2_4__group_3)
          & r2_hidden(C,c4_4__group_3) ) ) ),
    introduced(definition,[new_symbol(c7_4__group_3),file(group_3,c7_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c7_4__group_3)]).

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(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(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(d1_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) ) ) ) ),
    file(group_1,d1_group_1),
    [interesting(0.9),axiom,file(group_1,d1_group_1)]).

fof(d2_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k2_group_2(A,B,C) = a_3_0_group_2(A,B,C) ) ) ) ),
    file(group_2,d2_group_2),
    [interesting(0.9),axiom,file(group_2,d2_group_2)]).

fof(e3_4__group_3,plain,(
    ? [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_4__group_3))
      & ? [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_4__group_3))
          & c6_4__group_3 = k1_group_1(c1_4__group_3,A,B)
          & r2_hidden(A,c2_4__group_3)
          & r2_hidden(B,c4_4__group_3) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,e2_4__group_3])],[commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,dt_k1_funct_1,dt_k4_tarski,cc2_funct_1,rc1_funct_1,rc2_funct_1,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,fc4_subset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,existence_l1_group_1,existence_l1_struct_0,redefinition_k2_binop_1,dt_k1_zfmisc_1,dt_k2_binop_1,dt_l1_group_1,dt_l1_struct_0,dt_u1_group_1,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_group_1,dt_k2_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,t1_subset,t7_boole,d1_group_1,d2_group_2,e2_4__group_3]),
    [interesting(0.8),file(group_3,e3_4__group_3),[file(group_3,e3_4__group_3)]]).

fof(dt_c7_4__group_3,plain,(
    m1_subset_1(c7_4__group_3,u1_struct_0(c1_4__group_3)) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,e2_4__group_3])],[dh_c7_4__group_3,e3_4__group_3]),
    [interesting(0.8),file(group_3,c7_4__group_3),[file(group_3,c7_4__group_3)]]).

fof(dh_c8_4__group_3,definition,
    ( ? [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_4__group_3))
        & c6_4__group_3 = k1_group_1(c1_4__group_3,c7_4__group_3,A)
        & r2_hidden(c7_4__group_3,c2_4__group_3)
        & r2_hidden(A,c4_4__group_3) )
   => ( m1_subset_1(c8_4__group_3,u1_struct_0(c1_4__group_3))
      & c6_4__group_3 = k1_group_1(c1_4__group_3,c7_4__group_3,c8_4__group_3)
      & r2_hidden(c7_4__group_3,c2_4__group_3)
      & r2_hidden(c8_4__group_3,c4_4__group_3) ) ),
    introduced(definition,[new_symbol(c8_4__group_3),file(group_3,c8_4__group_3)]),
    [interesting(0.8),axiom,file(group_3,c8_4__group_3)]).

fof(dt_c8_4__group_3,plain,(
    m1_subset_1(c8_4__group_3,u1_struct_0(c1_4__group_3)) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,e2_4__group_3])],[dh_c7_4__group_3,dh_c8_4__group_3,e3_4__group_3]),
    [interesting(0.8),file(group_3,c8_4__group_3),[file(group_3,c8_4__group_3)]]).

fof(e4_4__group_3,plain,
    ( c6_4__group_3 = k1_group_1(c1_4__group_3,c7_4__group_3,c8_4__group_3)
    & r2_hidden(c7_4__group_3,c2_4__group_3)
    & r2_hidden(c8_4__group_3,c4_4__group_3) ),
    inference(consider,[status(thm),assumptions([dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,e2_4__group_3])],[dh_c7_4__group_3,dh_c8_4__group_3,e3_4__group_3]),
    [interesting(0.8),file(group_3,e4_4__group_3),[file(group_3,e4_4__group_3)]]).

fof(e5_4__group_3,plain,(
    r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_4__group_3,dt_c5_4__group_3,e1_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,e2_4__group_3])],[commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,dt_k1_funct_1,dt_k4_tarski,cc2_funct_1,rc1_funct_1,rc2_funct_1,d5_tarski,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_struct_0,fc1_xboole_0,fc4_subset_1,rc1_finset_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,d1_binop_1,existence_l1_group_1,existence_m1_subset_1,redefinition_k2_binop_1,dt_k1_zfmisc_1,dt_k2_binop_1,dt_l1_group_1,dt_m1_subset_1,dt_u1_group_1,dt_u1_struct_0,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_group_1,dt_k2_group_2,dt_c1_4__group_3,dt_c2_4__group_3,dt_c3_4__group_3,dt_c4_4__group_3,dt_c5_4__group_3,dt_c6_4__group_3,dt_c7_4__group_3,dt_c8_4__group_3,t1_subset,t3_subset,t7_boole,d1_group_1,d2_group_2,e1_4__group_3,e4_4__group_3]),
    [interesting(0.8),file(group_3,e5_4__group_3),[file(group_3,e5_4__group_3)]]).

fof(i9_4__group_3,theorem,(
    $true ),
    introduced(tautology,[file(group_3,i9_4__group_3)]),
    [interesting(0.8),trivial,file(group_3,i9_4__group_3)]).

fof(i8_4__group_3,plain,(
    r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_4__group_3,dt_c5_4__group_3,e1_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3,e2_4__group_3])],[e5_4__group_3,i9_4__group_3]),
    [interesting(0.8),file(group_3,i8_4__group_3),[file(group_3,i8_4__group_3)]]).

fof(i7_4__group_3,plain,(
    ~ ( r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3))
      & ~ r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_3,dt_c5_4__group_3,e1_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3,dt_c6_4__group_3]),discharge_asm(discharge,[e2_4__group_3])],[e2_4__group_3,i8_4__group_3]),
    [interesting(0.8),file(group_3,i7_4__group_3),[file(group_3,i7_4__group_3)]]).

fof(i7_4_tmp__group_3,plain,(
    ~ ( r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3))
      & ~ r2_hidden(c6_4__group_3,k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_3,dt_c5_4__group_3,e1_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3]),discharge_asm(discharge,[dt_c6_4__group_3])],[dt_c6_4__group_3,i7_4__group_3]),
    [interesting(0.8),i6_4__group_3]).

fof(i6_4__group_3,plain,(
    r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ),
    inference(let,[status(thm),assumptions([dt_c3_4__group_3,dt_c5_4__group_3,e1_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3])],[i7_4_tmp__group_3,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,dt_l1_struct_0,cc1_finset_1,cc1_funct_1,fc1_struct_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,fc1_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_group_2,dt_c1_4__group_3,dt_c2_4__group_3,dt_c3_4__group_3,dt_c4_4__group_3,dt_c5_4__group_3,d3_tarski,dh_c6_4__group_3]),
    [interesting(0.8),file(group_3,i6_4__group_3),[file(group_3,i6_4__group_3)]]).

fof(i5_4__group_3,plain,
    ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
      & r1_tarski(c4_4__group_3,c5_4__group_3) )
   => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_3,dt_c5_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3]),discharge_asm(discharge,[e1_4__group_3])],[e1_4__group_3,i6_4__group_3]),
    [interesting(0.8),file(group_3,i5_4__group_3),[file(group_3,i5_4__group_3)]]).

fof(i5_4_tmp__group_3,plain,
    ( m1_subset_1(c5_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
   => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
        & r1_tarski(c4_4__group_3,c5_4__group_3) )
     => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,c5_4__group_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3]),discharge_asm(discharge,[dt_c5_4__group_3])],[dt_c5_4__group_3,i5_4__group_3]),
    [interesting(0.8),i4_4__group_3]).

fof(i4_4__group_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
          & r1_tarski(c4_4__group_3,A) )
       => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3,dt_c4_4__group_3])],[i5_4_tmp__group_3,dh_c5_4__group_3]),
    [interesting(0.8),file(group_3,i4_4__group_3),[file(group_3,i4_4__group_3)]]).

fof(i4_4_tmp__group_3,plain,
    ( m1_subset_1(c4_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
            & r1_tarski(c4_4__group_3,A) )
         => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,c4_4__group_3),k2_group_2(c1_4__group_3,c3_4__group_3,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3]),discharge_asm(discharge,[dt_c4_4__group_3])],[dt_c4_4__group_3,i4_4__group_3]),
    [interesting(0.8),i3_4__group_3]).

fof(i3_4__group_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
              & r1_tarski(A,B) )
           => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,A),k2_group_2(c1_4__group_3,c3_4__group_3,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_4__group_3,dt_c1_4__group_3,dt_c2_4__group_3])],[i4_4_tmp__group_3,dh_c4_4__group_3]),
    [interesting(0.8),file(group_3,i3_4__group_3),[file(group_3,i3_4__group_3)]]).

fof(i3_4_tmp__group_3,plain,
    ( m1_subset_1(c3_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
           => ( ( r1_tarski(c2_4__group_3,c3_4__group_3)
                & r1_tarski(A,B) )
             => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,A),k2_group_2(c1_4__group_3,c3_4__group_3,B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__group_3,dt_c2_4__group_3]),discharge_asm(discharge,[dt_c3_4__group_3])],[dt_c3_4__group_3,i3_4__group_3]),
    [interesting(0.8),i2_4__group_3]).

fof(i2_4__group_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
             => ( ( r1_tarski(c2_4__group_3,A)
                  & r1_tarski(B,C) )
               => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,B),k2_group_2(c1_4__group_3,A,C)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__group_3,dt_c2_4__group_3])],[i3_4_tmp__group_3,dh_c3_4__group_3]),
    [interesting(0.8),file(group_3,i2_4__group_3),[file(group_3,i2_4__group_3)]]).

fof(i2_4_tmp__group_3,plain,
    ( m1_subset_1(c2_4__group_3,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
               => ( ( r1_tarski(c2_4__group_3,A)
                    & r1_tarski(B,C) )
                 => r1_tarski(k2_group_2(c1_4__group_3,c2_4__group_3,B),k2_group_2(c1_4__group_3,A,C)) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__group_3]),discharge_asm(discharge,[dt_c2_4__group_3])],[dt_c2_4__group_3,i2_4__group_3]),
    [interesting(0.8),i1_4__group_3]).

fof(i1_4__group_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
                 => ( ( r1_tarski(A,B)
                      & r1_tarski(C,D) )
                   => r1_tarski(k2_group_2(c1_4__group_3,A,C),k2_group_2(c1_4__group_3,B,D)) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__group_3])],[i2_4_tmp__group_3,dh_c2_4__group_3]),
    [interesting(0.8),file(group_3,i1_4__group_3),[file(group_3,i1_4__group_3)]]).

fof(i1_4_tmp__group_3,plain,
    ( ( ~ v3_struct_0(c1_4__group_3)
      & v3_group_1(c1_4__group_3)
      & v4_group_1(c1_4__group_3)
      & l1_group_1(c1_4__group_3) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_4__group_3)))
                   => ( ( r1_tarski(A,B)
                        & r1_tarski(C,D) )
                     => r1_tarski(k2_group_2(c1_4__group_3,A,C),k2_group_2(c1_4__group_3,B,D)) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__group_3])],[dt_c1_4__group_3,i1_4__group_3]),
    [interesting(1),t4_group_3]).

fof(t4_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,C)
                          & r1_tarski(D,E) )
                       => r1_tarski(k2_group_2(A,B,D),k2_group_2(A,C,E)) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__group_3,dh_c1_4__group_3]),
    [interesting(1),file(group_3,t4_group_3),[file(group_3,t4_group_3)]]).