% Mizar ND problem: t2_group_3,group_3,57,59 
fof(dh_c1_2__group_3,definition,
    ( ( ( ~ v3_struct_0(c1_2__group_3)
        & v3_group_1(c1_2__group_3)
        & v4_group_1(c1_2__group_3)
        & l1_group_1(c1_2__group_3) )
     => ( ( ~ v3_struct_0(c1_2__group_3)
          & v3_group_1(c1_2__group_3)
          & v4_group_1(c1_2__group_3)
          & v7_group_1(c1_2__group_3)
          & l1_group_1(c1_2__group_3) )
      <=> v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3)) ) )
   => ! [A] : 
        ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & l1_group_1(A) )
       => ( ( ~ v3_struct_0(A)
            & v3_group_1(A)
            & v4_group_1(A)
            & v7_group_1(A)
            & l1_group_1(A) )
        <=> v1_binop_1(u1_group_1(A),u1_struct_0(A)) ) ) ),
    introduced(definition,[new_symbol(c1_2__group_3),file(group_3,c1_2__group_3)]),
    [interesting(0.8),axiom,file(group_3,c1_2__group_3)]).

fof(e1_2_1__group_3,assumption,
    ( ~ v3_struct_0(c1_2__group_3)
    & v3_group_1(c1_2__group_3)
    & v4_group_1(c1_2__group_3)
    & v7_group_1(c1_2__group_3)
    & l1_group_1(c1_2__group_3) ),
    introduced(assumption,[file(group_3,e1_2_1__group_3)]),
    [interesting(0.65),axiom,file(group_3,e1_2_1__group_3)]).

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

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

fof(redefinition_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(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_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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_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_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_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(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_2__group_3,assumption,
    ( ~ v3_struct_0(c1_2__group_3)
    & v3_group_1(c1_2__group_3)
    & v4_group_1(c1_2__group_3)
    & l1_group_1(c1_2__group_3) ),
    introduced(assumption,[file(group_3,c1_2__group_3)]),
    [interesting(0.8),axiom,file(group_3,c1_2__group_3)]).

fof(dt_c1_2_1__group_3,assumption,(
    m1_subset_1(c1_2_1__group_3,u1_struct_0(c1_2__group_3)) ),
    introduced(assumption,[file(group_3,c1_2_1__group_3)]),
    [interesting(0.65),axiom,file(group_3,c1_2_1__group_3)]).

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(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_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_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(d13_binop_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v1_binop_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,A)
                   => k2_binop_1(A,A,A,B,C,D) = k2_binop_1(A,A,A,B,D,C) ) ) ) ) ) ),
    file(binop_1,d13_binop_1),
    [interesting(0.9),axiom,file(binop_1,d13_binop_1)]).

fof(dh_c1_2_1__group_3,definition,
    ( ( m1_subset_1(c1_2_1__group_3,u1_struct_0(c1_2__group_3))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
         => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,A) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),A,c1_2_1__group_3) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_2__group_3))
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c1_2__group_3))
           => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),B,C) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),C,B) ) ) ),
    introduced(definition,[new_symbol(c1_2_1__group_3),file(group_3,c1_2_1__group_3)]),
    [interesting(0.65),axiom,file(group_3,c1_2_1__group_3)]).

fof(dh_c2_2_1__group_3,definition,
    ( ( m1_subset_1(c2_2_1__group_3,u1_struct_0(c1_2__group_3))
     => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,c2_2_1__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_1__group_3,c1_2_1__group_3) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
       => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,A) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),A,c1_2_1__group_3) ) ),
    introduced(definition,[new_symbol(c2_2_1__group_3),file(group_3,c2_2_1__group_3)]),
    [interesting(0.65),axiom,file(group_3,c2_2_1__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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_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(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

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

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

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

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

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

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

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

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

fof(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(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_c2_2_1__group_3,assumption,(
    m1_subset_1(c2_2_1__group_3,u1_struct_0(c1_2__group_3)) ),
    introduced(assumption,[file(group_3,c2_2_1__group_3)]),
    [interesting(0.65),axiom,file(group_3,c2_2_1__group_3)]).

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(e1_2_1_1__group_3,plain,(
    k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,c2_2_1__group_3) = k1_group_1(c1_2__group_3,c1_2_1__group_3,c2_2_1__group_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_l1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,redefinition_k2_binop_1,dt_k1_group_1,dt_k2_binop_1,dt_u1_group_1,dt_u1_struct_0,dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3,d1_group_1]),
    [interesting(0.5),file(group_3,e1_2_1_1__group_3),[file(group_3,e1_2_1_1__group_3)]]).

fof(commutativity_k10_group_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k10_group_1(A,B,C) = k10_group_1(A,C,B) ) ),
    file(group_1,k10_group_1),
    [interesting(0.9),axiom,file(group_1,k10_group_1)]).

fof(redefinition_k10_group_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k10_group_1(A,B,C) = k1_group_1(A,B,C) ) ),
    file(group_1,k10_group_1),
    [interesting(0.9),axiom,file(group_1,k10_group_1)]).

fof(dt_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k10_group_1),
    [interesting(0.9),axiom,file(group_1,k10_group_1)]).

fof(l2_group_3,plain,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_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))
             => k10_group_1(A,B,C) = k10_group_1(A,C,B) ) ) ) ),
    file(group_3,l2_group_3),
    [interesting(0.9),axiom,file(group_3,l2_group_3)]).

fof(e2_2_1_1__group_3,plain,(
    k1_group_1(c1_2__group_3,c1_2_1__group_3,c2_2_1__group_3) = k1_group_1(c1_2__group_3,c2_2_1__group_3,c1_2_1__group_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3,e1_2_1__group_3])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,existence_l1_struct_0,redefinition_k2_binop_1,dt_k2_binop_1,dt_l1_struct_0,dt_u1_group_1,fc1_struct_0,rc3_struct_0,commutativity_k10_group_1,existence_l1_group_1,existence_m1_subset_1,redefinition_k10_group_1,dt_k10_group_1,dt_k1_group_1,dt_l1_group_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3,cc1_group_1,d1_group_1,e1_2_1__group_3,l2_group_3]),
    [interesting(0.5),file(group_3,e2_2_1_1__group_3),[file(group_3,e2_2_1_1__group_3)]]).

fof(e3_2_1_1__group_3,plain,(
    k1_group_1(c1_2__group_3,c2_2_1__group_3,c1_2_1__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_1__group_3,c1_2_1__group_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_l1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,redefinition_k2_binop_1,dt_k1_group_1,dt_k2_binop_1,dt_u1_group_1,dt_u1_struct_0,dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3,d1_group_1]),
    [interesting(0.5),file(group_3,e3_2_1_1__group_3),[file(group_3,e3_2_1_1__group_3)]]).

fof(e2_2_1__group_3,plain,(
    k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,c2_2_1__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_1__group_3,c1_2_1__group_3) ),
    inference(iterative_eq,[status(thm),assumptions([e1_2_1__group_3,dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3])],[e1_2_1_1__group_3,e2_2_1_1__group_3,e3_2_1_1__group_3]),
    [interesting(0.65),file(group_3,e2_2_1__group_3),[file(group_3,e2_2_1__group_3)]]).

fof(i4_2_1__group_3,theorem,(
    $true ),
    introduced(tautology,[file(group_3,i4_2_1__group_3)]),
    [interesting(0.65),trivial,file(group_3,i4_2_1__group_3)]).

fof(i3_2_1__group_3,plain,(
    k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,c2_2_1__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_1__group_3,c1_2_1__group_3) ),
    inference(conclusion,[status(thm),assumptions([e1_2_1__group_3,dt_c1_2__group_3,dt_c1_2_1__group_3,dt_c2_2_1__group_3])],[e2_2_1__group_3,i4_2_1__group_3]),
    [interesting(0.65),file(group_3,i3_2_1__group_3),[file(group_3,i3_2_1__group_3)]]).

fof(i3_2_1_tmp__group_3,plain,
    ( m1_subset_1(c2_2_1__group_3,u1_struct_0(c1_2__group_3))
   => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,c2_2_1__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_1__group_3,c1_2_1__group_3) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2_1__group_3,dt_c1_2__group_3,dt_c1_2_1__group_3]),discharge_asm(discharge,[dt_c2_2_1__group_3])],[dt_c2_2_1__group_3,i3_2_1__group_3]),
    [interesting(0.65),i2_2_1__group_3]).

fof(i2_2_1__group_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
     => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,A) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),A,c1_2_1__group_3) ) ),
    inference(let,[status(thm),assumptions([e1_2_1__group_3,dt_c1_2__group_3,dt_c1_2_1__group_3])],[i3_2_1_tmp__group_3,dh_c2_2_1__group_3]),
    [interesting(0.65),file(group_3,i2_2_1__group_3),[file(group_3,i2_2_1__group_3)]]).

fof(i2_2_1_tmp__group_3,plain,
    ( m1_subset_1(c1_2_1__group_3,u1_struct_0(c1_2__group_3))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
       => k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_1__group_3,A) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),A,c1_2_1__group_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2_1__group_3,dt_c1_2__group_3]),discharge_asm(discharge,[dt_c1_2_1__group_3])],[dt_c1_2_1__group_3,i2_2_1__group_3]),
    [interesting(0.65),i1_2_1__group_3]).

fof(i1_2_1__group_3,plain,(
    v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3)) ),
    inference(let,[status(thm),assumptions([e1_2_1__group_3,dt_c1_2__group_3])],[i2_2_1_tmp__group_3,rc3_funct_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,dt_k1_binop_1,dt_k1_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_relset_1,cc1_group_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_struct_0,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,redefinition_k2_binop_1,redefinition_m2_relset_1,dt_k2_binop_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_group_1,dt_u1_struct_0,dt_c1_2__group_3,cc1_finset_1,cc1_funct_1,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,d13_binop_1,dh_c1_2_1__group_3]),
    [interesting(0.65),file(group_3,i1_2_1__group_3),[file(group_3,i1_2_1__group_3)]]).

fof(e1_2__group_3,plain,
    ( ( ~ v3_struct_0(c1_2__group_3)
      & v3_group_1(c1_2__group_3)
      & v4_group_1(c1_2__group_3)
      & v7_group_1(c1_2__group_3)
      & l1_group_1(c1_2__group_3) )
   => v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__group_3]),discharge_asm(discharge,[e1_2_1__group_3])],[e1_2_1__group_3,i1_2_1__group_3]),
    [interesting(0.8),file(group_3,e1_2__group_3),[file(group_3,e1_2__group_3)]]).

fof(e2_2__group_3,assumption,(
    v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3)) ),
    introduced(assumption,[file(group_3,e2_2__group_3)]),
    [interesting(0.8),axiom,file(group_3,e2_2__group_3)]).

fof(dt_c1_2_2__group_3,assumption,(
    m1_subset_1(c1_2_2__group_3,u1_struct_0(c1_2__group_3)) ),
    introduced(assumption,[file(group_3,c1_2_2__group_3)]),
    [interesting(0.65),axiom,file(group_3,c1_2_2__group_3)]).

fof(d16_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v7_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) = k1_group_1(A,C,B) ) ) ) ) ),
    file(group_1,d16_group_1),
    [interesting(0.9),axiom,file(group_1,d16_group_1)]).

fof(dh_c1_2_2__group_3,definition,
    ( ( m1_subset_1(c1_2_2__group_3,u1_struct_0(c1_2__group_3))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
         => k1_group_1(c1_2__group_3,c1_2_2__group_3,A) = k1_group_1(c1_2__group_3,A,c1_2_2__group_3) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_2__group_3))
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c1_2__group_3))
           => k1_group_1(c1_2__group_3,B,C) = k1_group_1(c1_2__group_3,C,B) ) ) ),
    introduced(definition,[new_symbol(c1_2_2__group_3),file(group_3,c1_2_2__group_3)]),
    [interesting(0.65),axiom,file(group_3,c1_2_2__group_3)]).

fof(dh_c2_2_2__group_3,definition,
    ( ( m1_subset_1(c2_2_2__group_3,u1_struct_0(c1_2__group_3))
     => k1_group_1(c1_2__group_3,c1_2_2__group_3,c2_2_2__group_3) = k1_group_1(c1_2__group_3,c2_2_2__group_3,c1_2_2__group_3) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
       => k1_group_1(c1_2__group_3,c1_2_2__group_3,A) = k1_group_1(c1_2__group_3,A,c1_2_2__group_3) ) ),
    introduced(definition,[new_symbol(c2_2_2__group_3),file(group_3,c2_2_2__group_3)]),
    [interesting(0.65),axiom,file(group_3,c2_2_2__group_3)]).

fof(dt_c2_2_2__group_3,assumption,(
    m1_subset_1(c2_2_2__group_3,u1_struct_0(c1_2__group_3)) ),
    introduced(assumption,[file(group_3,c2_2_2__group_3)]),
    [interesting(0.65),axiom,file(group_3,c2_2_2__group_3)]).

fof(e1_2_2_1__group_3,plain,(
    k1_group_1(c1_2__group_3,c1_2_2__group_3,c2_2_2__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_2__group_3,c2_2_2__group_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_l1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,redefinition_k2_binop_1,dt_k1_group_1,dt_k2_binop_1,dt_u1_group_1,dt_u1_struct_0,dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3,d1_group_1]),
    [interesting(0.5),file(group_3,e1_2_2_1__group_3),[file(group_3,e1_2_2_1__group_3)]]).

fof(d2_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => ! [D] : 
                ( m1_subset_1(D,A)
               => k1_binop_1(B,C,D) = k1_binop_1(B,D,C) ) ) ) ) ),
    file(binop_1,d2_binop_1),
    [interesting(0.9),axiom,file(binop_1,d2_binop_1)]).

fof(e2_2_2_1__group_3,plain,(
    k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c1_2_2__group_3,c2_2_2__group_3) = k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_2__group_3,c1_2_2__group_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3,e2_2__group_3])],[commutativity_k2_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,cc2_finset_1,fc14_finset_1,fc1_finset_1,fc1_xboole_0,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_finset_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_l1_group_1,existence_l1_struct_0,existence_m1_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_tarski,dt_l1_group_1,dt_l1_struct_0,dt_m1_relset_1,cc1_finset_1,cc1_funct_1,cc1_group_1,cc1_relset_1,cc2_funct_1,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d5_tarski,existence_m1_subset_1,existence_m2_relset_1,redefinition_k2_binop_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_binop_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_group_1,dt_u1_struct_0,dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3,d1_binop_1,e2_2__group_3,d2_binop_1]),
    [interesting(0.5),file(group_3,e2_2_2_1__group_3),[file(group_3,e2_2_2_1__group_3)]]).

fof(e3_2_2_1__group_3,plain,(
    k2_binop_1(u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_struct_0(c1_2__group_3),u1_group_1(c1_2__group_3),c2_2_2__group_3,c1_2_2__group_3) = k1_group_1(c1_2__group_3,c2_2_2__group_3,c1_2_2__group_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_l1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,fc4_subset_1,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,redefinition_k2_binop_1,dt_k1_group_1,dt_k2_binop_1,dt_u1_group_1,dt_u1_struct_0,dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3,d1_group_1]),
    [interesting(0.5),file(group_3,e3_2_2_1__group_3),[file(group_3,e3_2_2_1__group_3)]]).

fof(e1_2_2__group_3,plain,(
    k1_group_1(c1_2__group_3,c1_2_2__group_3,c2_2_2__group_3) = k1_group_1(c1_2__group_3,c2_2_2__group_3,c1_2_2__group_3) ),
    inference(iterative_eq,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3])],[e1_2_2_1__group_3,e2_2_2_1__group_3,e3_2_2_1__group_3]),
    [interesting(0.65),file(group_3,e1_2_2__group_3),[file(group_3,e1_2_2__group_3)]]).

fof(i3_2_2__group_3,theorem,(
    $true ),
    introduced(tautology,[file(group_3,i3_2_2__group_3)]),
    [interesting(0.65),trivial,file(group_3,i3_2_2__group_3)]).

fof(i2_2_2__group_3,plain,(
    k1_group_1(c1_2__group_3,c1_2_2__group_3,c2_2_2__group_3) = k1_group_1(c1_2__group_3,c2_2_2__group_3,c1_2_2__group_3) ),
    inference(conclusion,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3,dt_c1_2_2__group_3,dt_c2_2_2__group_3])],[e1_2_2__group_3,i3_2_2__group_3]),
    [interesting(0.65),file(group_3,i2_2_2__group_3),[file(group_3,i2_2_2__group_3)]]).

fof(i2_2_2_tmp__group_3,plain,
    ( m1_subset_1(c2_2_2__group_3,u1_struct_0(c1_2__group_3))
   => k1_group_1(c1_2__group_3,c1_2_2__group_3,c2_2_2__group_3) = k1_group_1(c1_2__group_3,c2_2_2__group_3,c1_2_2__group_3) ),
    inference(discharge_asm,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3,dt_c1_2_2__group_3]),discharge_asm(discharge,[dt_c2_2_2__group_3])],[dt_c2_2_2__group_3,i2_2_2__group_3]),
    [interesting(0.65),i1_2_2__group_3]).

fof(i1_2_2__group_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
     => k1_group_1(c1_2__group_3,c1_2_2__group_3,A) = k1_group_1(c1_2__group_3,A,c1_2_2__group_3) ) ),
    inference(let,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3,dt_c1_2_2__group_3])],[i2_2_2_tmp__group_3,dh_c2_2_2__group_3]),
    [interesting(0.65),file(group_3,i1_2_2__group_3),[file(group_3,i1_2_2__group_3)]]).

fof(i1_2_2_tmp__group_3,plain,
    ( m1_subset_1(c1_2_2__group_3,u1_struct_0(c1_2__group_3))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_2__group_3))
       => k1_group_1(c1_2__group_3,c1_2_2__group_3,A) = k1_group_1(c1_2__group_3,A,c1_2_2__group_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3]),discharge_asm(discharge,[dt_c1_2_2__group_3])],[dt_c1_2_2__group_3,i1_2_2__group_3]),
    [interesting(0.8),e3_2__group_3]).

fof(e3_2__group_3,plain,(
    v7_group_1(c1_2__group_3) ),
    inference(let,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3])],[i1_2_2_tmp__group_3,rc1_finset_1,cc1_finset_1,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,dt_l1_struct_0,cc1_group_1,fc1_struct_0,rc3_struct_0,dt_k1_group_1,dt_l1_group_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_2__group_3,d16_group_1,dh_c1_2_2__group_3]),
    [interesting(0.8),file(group_3,e3_2__group_3),[file(group_3,e3_2__group_3)]]).

fof(e4_2__group_3,plain,
    ( ~ v3_struct_0(c1_2__group_3)
    & v3_group_1(c1_2__group_3)
    & v4_group_1(c1_2__group_3)
    & v7_group_1(c1_2__group_3)
    & l1_group_1(c1_2__group_3) ),
    inference(mizar_by,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3])],[existence_l1_struct_0,dt_l1_struct_0,rc3_struct_0,existence_l1_group_1,dt_l1_group_1,dt_c1_2__group_3,cc1_group_1,e3_2__group_3]),
    [interesting(0.8),file(group_3,e4_2__group_3),[file(group_3,e4_2__group_3)]]).

fof(i4_2__group_3,theorem,(
    $true ),
    introduced(tautology,[file(group_3,i4_2__group_3)]),
    [interesting(0.8),trivial,file(group_3,i4_2__group_3)]).

fof(i3_2__group_3,plain,
    ( ~ v3_struct_0(c1_2__group_3)
    & v3_group_1(c1_2__group_3)
    & v4_group_1(c1_2__group_3)
    & v7_group_1(c1_2__group_3)
    & l1_group_1(c1_2__group_3) ),
    inference(conclusion,[status(thm),assumptions([e2_2__group_3,dt_c1_2__group_3])],[e4_2__group_3,i4_2__group_3]),
    [interesting(0.8),file(group_3,i3_2__group_3),[file(group_3,i3_2__group_3)]]).

fof(i2_2__group_3,plain,
    ( v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3))
   => ( ~ v3_struct_0(c1_2__group_3)
      & v3_group_1(c1_2__group_3)
      & v4_group_1(c1_2__group_3)
      & v7_group_1(c1_2__group_3)
      & l1_group_1(c1_2__group_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__group_3]),discharge_asm(discharge,[e2_2__group_3])],[e2_2__group_3,i3_2__group_3]),
    [interesting(0.8),file(group_3,i2_2__group_3),[file(group_3,i2_2__group_3)]]).

fof(i1_2__group_3,plain,
    ( ( ~ v3_struct_0(c1_2__group_3)
      & v3_group_1(c1_2__group_3)
      & v4_group_1(c1_2__group_3)
      & v7_group_1(c1_2__group_3)
      & l1_group_1(c1_2__group_3) )
  <=> v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2__group_3])],[e1_2__group_3,i2_2__group_3]),
    [interesting(0.8),file(group_3,i1_2__group_3),[file(group_3,i1_2__group_3)]]).

fof(i1_2_tmp__group_3,plain,
    ( ( ~ v3_struct_0(c1_2__group_3)
      & v3_group_1(c1_2__group_3)
      & v4_group_1(c1_2__group_3)
      & l1_group_1(c1_2__group_3) )
   => ( ( ~ v3_struct_0(c1_2__group_3)
        & v3_group_1(c1_2__group_3)
        & v4_group_1(c1_2__group_3)
        & v7_group_1(c1_2__group_3)
        & l1_group_1(c1_2__group_3) )
    <=> v1_binop_1(u1_group_1(c1_2__group_3),u1_struct_0(c1_2__group_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__group_3])],[dt_c1_2__group_3,i1_2__group_3]),
    [interesting(1),t2_group_3]).

fof(t2_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> v1_binop_1(u1_group_1(A),u1_struct_0(A)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__group_3,dh_c1_2__group_3]),
    [interesting(1),file(group_3,t2_group_3),[file(group_3,t2_group_3)]]).