% Mizar ND problem: t6_group_6,group_6,141,39 
fof(dh_c1_7__group_6,definition,
    ( ( ( ~ v3_struct_0(c1_7__group_6)
        & v3_group_1(c1_7__group_6)
        & v4_group_1(c1_7__group_6)
        & l1_group_1(c1_7__group_6) )
     => ! [A] : 
          ( m1_group_2(A,c1_7__group_6)
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_7__group_6))
             => ( k10_group_2(c1_7__group_6,A,k12_group_2(c1_7__group_6,A,B)) = k12_group_2(c1_7__group_6,A,B)
                & k3_group_2(c1_7__group_6,B,k7_group_4(c1_7__group_6,A,A)) = k12_group_2(c1_7__group_6,A,B)
                & k4_group_2(c1_7__group_6,B,k7_group_4(c1_7__group_6,A,A)) = k13_group_2(c1_7__group_6,A,B)
                & k11_group_2(c1_7__group_6,A,k13_group_2(c1_7__group_6,A,B)) = k13_group_2(c1_7__group_6,A,B) ) ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & v3_group_1(C)
          & v4_group_1(C)
          & l1_group_1(C) )
       => ! [D] : 
            ( m1_group_2(D,C)
           => ! [E] : 
                ( m1_subset_1(E,u1_struct_0(C))
               => ( k10_group_2(C,D,k12_group_2(C,D,E)) = k12_group_2(C,D,E)
                  & k3_group_2(C,E,k7_group_4(C,D,D)) = k12_group_2(C,D,E)
                  & k4_group_2(C,E,k7_group_4(C,D,D)) = k13_group_2(C,D,E)
                  & k11_group_2(C,D,k13_group_2(C,D,E)) = k13_group_2(C,D,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_7__group_6),file(group_6,c1_7__group_6)]),
    [interesting(0.8),axiom,file(group_6,c1_7__group_6)]).

fof(dh_c2_7__group_6,definition,
    ( ( m1_group_2(c2_7__group_6,c1_7__group_6)
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_7__group_6))
         => ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,A)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
            & k3_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
            & k4_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,A)
            & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,A)) = k13_group_2(c1_7__group_6,c2_7__group_6,A) ) ) )
   => ! [B] : 
        ( m1_group_2(B,c1_7__group_6)
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c1_7__group_6))
           => ( k10_group_2(c1_7__group_6,B,k12_group_2(c1_7__group_6,B,C)) = k12_group_2(c1_7__group_6,B,C)
              & k3_group_2(c1_7__group_6,C,k7_group_4(c1_7__group_6,B,B)) = k12_group_2(c1_7__group_6,B,C)
              & k4_group_2(c1_7__group_6,C,k7_group_4(c1_7__group_6,B,B)) = k13_group_2(c1_7__group_6,B,C)
              & k11_group_2(c1_7__group_6,B,k13_group_2(c1_7__group_6,B,C)) = k13_group_2(c1_7__group_6,B,C) ) ) ) ),
    introduced(definition,[new_symbol(c2_7__group_6),file(group_6,c2_7__group_6)]),
    [interesting(0.8),axiom,file(group_6,c2_7__group_6)]).

fof(dh_c3_7__group_6,definition,
    ( ( m1_subset_1(c3_7__group_6,u1_struct_0(c1_7__group_6))
     => ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
        & k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
        & k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
        & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_7__group_6))
       => ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,A)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
          & k3_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
          & k4_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,A)
          & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,A)) = k13_group_2(c1_7__group_6,c2_7__group_6,A) ) ) ),
    introduced(definition,[new_symbol(c3_7__group_6),file(group_6,c3_7__group_6)]),
    [interesting(0.8),axiom,file(group_6,c3_7__group_6)]).

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_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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(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(cc1_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

fof(rc1_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

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_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_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(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

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

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

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

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

fof(d1_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(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(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(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(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(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

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

fof(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(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(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(redefinition_k6_domain_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_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_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_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    [interesting(0.9),axiom,file(domain_1,k6_domain_1)]).

fof(dt_k7_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => m1_subset_1(k7_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k7_group_2),
    [interesting(0.9),axiom,file(group_2,k7_group_2)]).

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

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

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

fof(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(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(d9_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => k7_group_2(A,B) = u1_struct_0(B) ) ) ),
    file(group_2,d9_group_2),
    [interesting(0.9),axiom,file(group_2,d9_group_2)]).

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_k10_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k10_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k10_group_2),
    [interesting(0.9),axiom,file(group_2,k10_group_2)]).

fof(dt_k12_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k12_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k12_group_2),
    [interesting(0.9),axiom,file(group_2,k12_group_2)]).

fof(dt_k3_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k3_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k3_group_2),
    [interesting(0.9),axiom,file(group_2,k3_group_2)]).

fof(dt_k7_group_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => m1_subset_1(k7_group_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_4,k7_group_4),
    [interesting(0.9),axiom,file(group_4,k7_group_4)]).

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(dt_c1_7__group_6,assumption,
    ( ~ v3_struct_0(c1_7__group_6)
    & v3_group_1(c1_7__group_6)
    & v4_group_1(c1_7__group_6)
    & l1_group_1(c1_7__group_6) ),
    introduced(assumption,[file(group_6,c1_7__group_6)]),
    [interesting(0.8),axiom,file(group_6,c1_7__group_6)]).

fof(dt_c2_7__group_6,assumption,(
    m1_group_2(c2_7__group_6,c1_7__group_6) ),
    introduced(assumption,[file(group_6,c2_7__group_6)]),
    [interesting(0.8),axiom,file(group_6,c2_7__group_6)]).

fof(dt_c3_7__group_6,assumption,(
    m1_subset_1(c3_7__group_6,u1_struct_0(c1_7__group_6)) ),
    introduced(assumption,[file(group_6,c3_7__group_6)]),
    [interesting(0.8),axiom,file(group_6,c3_7__group_6)]).

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(d11_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k10_group_2(A,B,C) = k2_group_2(A,C,k7_group_2(A,B)) ) ) ) ),
    file(group_2,d11_group_2),
    [interesting(0.9),axiom,file(group_2,d11_group_2)]).

fof(d13_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_group_2(A,B,C) = k3_group_2(A,C,k7_group_2(A,B)) ) ) ) ),
    file(group_2,d13_group_2),
    [interesting(0.9),axiom,file(group_2,d13_group_2)]).

fof(d3_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k3_group_2(A,B,C) = k2_group_2(A,k6_domain_1(u1_struct_0(A),B),C) ) ) ) ),
    file(group_2,d3_group_2),
    [interesting(0.9),axiom,file(group_2,d3_group_2)]).

fof(t60_group_4,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_group_2(C,A)
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => k10_group_2(A,D,k12_group_2(A,C,B)) = k3_group_2(A,B,k7_group_4(A,C,D)) ) ) ) ) ),
    file(group_4,t60_group_4),
    [interesting(0.9),axiom,file(group_4,t60_group_4)]).

fof(e1_7_1__group_6,plain,(
    k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,dt_k1_tarski,cc1_finset_1,fc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_struct_0,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_k7_group_2,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,t3_subset,d2_group_2,d9_group_2,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k10_group_2,dt_k12_group_2,dt_k3_group_2,dt_k7_group_4,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,cc1_group_1,cc1_group_2,d11_group_2,d13_group_2,d3_group_2,t60_group_4]),
    [interesting(0.65),file(group_6,e1_7_1__group_6),[file(group_6,e1_7_1__group_6)]]).

fof(t58_group_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => k7_group_4(A,B,B) = k7_group_2(A,B) ) ) ),
    file(group_4,t58_group_4),
    [interesting(0.9),axiom,file(group_4,t58_group_4)]).

fof(e2_7_1__group_6,plain,(
    k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_2(c1_7__group_6,c2_7__group_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,dt_k1_tarski,cc1_finset_1,fc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_struct_0,existence_m1_subset_1,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,fc1_struct_0,rc3_struct_0,t3_subset,d2_group_2,existence_l1_group_1,existence_m1_group_2,dt_k3_group_2,dt_k7_group_2,dt_k7_group_4,dt_l1_group_1,dt_m1_group_2,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,cc1_group_1,cc1_group_2,d3_group_2,d9_group_2,t58_group_4]),
    [interesting(0.65),file(group_6,e2_7_1__group_6),[file(group_6,e2_7_1__group_6)]]).

fof(e3_7_1__group_6,plain,(
    k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_2(c1_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,existence_l1_struct_0,dt_k1_tarski,dt_l1_struct_0,cc1_finset_1,fc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,t3_subset,d2_group_2,dt_k12_group_2,dt_k3_group_2,dt_k7_group_2,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,d13_group_2,d3_group_2,d9_group_2]),
    [interesting(0.65),file(group_6,e3_7_1__group_6),[file(group_6,e3_7_1__group_6)]]).

fof(e1_7__group_6,plain,(
    k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[e1_7_1__group_6,e2_7_1__group_6,e3_7_1__group_6]),
    [interesting(0.8),file(group_6,e1_7__group_6),[file(group_6,e1_7__group_6)]]).

fof(e2_7__group_6,plain,(
    k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,dt_k1_tarski,cc1_finset_1,fc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_struct_0,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_k7_group_2,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,t3_subset,d2_group_2,d9_group_2,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k10_group_2,dt_k12_group_2,dt_k3_group_2,dt_k7_group_4,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,cc1_group_1,cc1_group_2,d11_group_2,d13_group_2,d3_group_2,e1_7__group_6,t60_group_4]),
    [interesting(0.8),file(group_6,e2_7__group_6),[file(group_6,e2_7__group_6)]]).

fof(dt_k4_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k4_group_2),
    [interesting(0.9),axiom,file(group_2,k4_group_2)]).

fof(d4_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_group_2(A,B,C) = k2_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) ),
    file(group_2,d4_group_2),
    [interesting(0.9),axiom,file(group_2,d4_group_2)]).

fof(e1_7_2__group_6,plain,(
    k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_2(c1_7__group_6,c2_7__group_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,dt_k1_tarski,cc1_finset_1,fc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_struct_0,existence_m1_subset_1,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,fc1_struct_0,rc3_struct_0,t3_subset,d2_group_2,existence_l1_group_1,existence_m1_group_2,dt_k4_group_2,dt_k7_group_2,dt_k7_group_4,dt_l1_group_1,dt_m1_group_2,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,cc1_group_1,cc1_group_2,d4_group_2,d9_group_2,t58_group_4]),
    [interesting(0.65),file(group_6,e1_7_2__group_6),[file(group_6,e1_7_2__group_6)]]).

fof(dt_k13_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k13_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k13_group_2),
    [interesting(0.9),axiom,file(group_2,k13_group_2)]).

fof(d14_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k13_group_2(A,B,C) = k4_group_2(A,C,k7_group_2(A,B)) ) ) ) ),
    file(group_2,d14_group_2),
    [interesting(0.9),axiom,file(group_2,d14_group_2)]).

fof(e2_7_2__group_6,plain,(
    k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_2(c1_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,existence_l1_struct_0,dt_k1_tarski,dt_l1_struct_0,cc1_finset_1,fc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,t3_subset,d2_group_2,dt_k13_group_2,dt_k4_group_2,dt_k7_group_2,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,d14_group_2,d4_group_2,d9_group_2]),
    [interesting(0.65),file(group_6,e2_7_2__group_6),[file(group_6,e2_7_2__group_6)]]).

fof(e3_7__group_6,plain,(
    k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[e1_7_2__group_6,e2_7_2__group_6]),
    [interesting(0.8),file(group_6,e3_7__group_6),[file(group_6,e3_7__group_6)]]).

fof(dt_k11_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k11_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k11_group_2),
    [interesting(0.9),axiom,file(group_2,k11_group_2)]).

fof(d12_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k11_group_2(A,B,C) = k2_group_2(A,k7_group_2(A,B),C) ) ) ) ),
    file(group_2,d12_group_2),
    [interesting(0.9),axiom,file(group_2,d12_group_2)]).

fof(t61_group_4,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_group_2(C,A)
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => k4_group_2(A,B,k7_group_4(A,C,D)) = k11_group_2(A,C,k13_group_2(A,D,B)) ) ) ) ) ),
    file(group_4,t61_group_4),
    [interesting(0.9),axiom,file(group_4,t61_group_4)]).

fof(e4_7__group_6,plain,(
    k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k4_tarski,cc1_funct_2,rc1_funct_2,rc2_partfun1,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_relset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,d1_binop_1,redefinition_k2_binop_1,dt_k2_binop_1,dt_u1_group_1,antisymmetry_r2_hidden,dt_k1_group_1,dt_k1_xboole_0,cc2_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,d1_group_1,reflexivity_r1_tarski,dt_k1_tarski,cc1_finset_1,fc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_3_0_group_2,existence_l1_struct_0,redefinition_k6_domain_1,dt_k1_zfmisc_1,dt_k2_group_2,dt_k6_domain_1,dt_k7_group_2,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,t3_subset,d2_group_2,d9_group_2,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k11_group_2,dt_k13_group_2,dt_k4_group_2,dt_k7_group_4,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6,cc1_group_1,cc1_group_2,d12_group_2,d14_group_2,d4_group_2,e3_7__group_6,t61_group_4]),
    [interesting(0.8),file(group_6,e4_7__group_6),[file(group_6,e4_7__group_6)]]).

fof(i7_7__group_6,theorem,(
    $true ),
    introduced(tautology,[file(group_6,i7_7__group_6)]),
    [interesting(0.8),trivial,file(group_6,i7_7__group_6)]).

fof(i6_7__group_6,plain,(
    k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[e4_7__group_6,i7_7__group_6]),
    [interesting(0.8),file(group_6,i6_7__group_6),[file(group_6,i6_7__group_6)]]).

fof(i5_7__group_6,plain,
    ( k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
    & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[e3_7__group_6,i6_7__group_6]),
    [interesting(0.8),file(group_6,i5_7__group_6),[file(group_6,i5_7__group_6)]]).

fof(i4_7__group_6,plain,
    ( k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
    & k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
    & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[e2_7__group_6,i5_7__group_6]),
    [interesting(0.8),file(group_6,i4_7__group_6),[file(group_6,i4_7__group_6)]]).

fof(i3_7__group_6,plain,
    ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
    & k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
    & k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
    & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6,dt_c3_7__group_6])],[e1_7__group_6,i4_7__group_6]),
    [interesting(0.8),file(group_6,i3_7__group_6),[file(group_6,i3_7__group_6)]]).

fof(i3_7_tmp__group_6,plain,
    ( m1_subset_1(c3_7__group_6,u1_struct_0(c1_7__group_6))
   => ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
      & k3_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
      & k4_group_2(c1_7__group_6,c3_7__group_6,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)
      & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,c3_7__group_6) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6]),discharge_asm(discharge,[dt_c3_7__group_6])],[dt_c3_7__group_6,i3_7__group_6]),
    [interesting(0.8),i2_7__group_6]).

fof(i2_7__group_6,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_7__group_6))
     => ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,A)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
        & k3_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
        & k4_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,A)
        & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,A)) = k13_group_2(c1_7__group_6,c2_7__group_6,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__group_6,dt_c2_7__group_6])],[i3_7_tmp__group_6,dh_c3_7__group_6]),
    [interesting(0.8),file(group_6,i2_7__group_6),[file(group_6,i2_7__group_6)]]).

fof(i2_7_tmp__group_6,plain,
    ( m1_group_2(c2_7__group_6,c1_7__group_6)
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_7__group_6))
       => ( k10_group_2(c1_7__group_6,c2_7__group_6,k12_group_2(c1_7__group_6,c2_7__group_6,A)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
          & k3_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k12_group_2(c1_7__group_6,c2_7__group_6,A)
          & k4_group_2(c1_7__group_6,A,k7_group_4(c1_7__group_6,c2_7__group_6,c2_7__group_6)) = k13_group_2(c1_7__group_6,c2_7__group_6,A)
          & k11_group_2(c1_7__group_6,c2_7__group_6,k13_group_2(c1_7__group_6,c2_7__group_6,A)) = k13_group_2(c1_7__group_6,c2_7__group_6,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__group_6]),discharge_asm(discharge,[dt_c2_7__group_6])],[dt_c2_7__group_6,i2_7__group_6]),
    [interesting(0.8),i1_7__group_6]).

fof(i1_7__group_6,plain,(
    ! [A] : 
      ( m1_group_2(A,c1_7__group_6)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_7__group_6))
         => ( k10_group_2(c1_7__group_6,A,k12_group_2(c1_7__group_6,A,B)) = k12_group_2(c1_7__group_6,A,B)
            & k3_group_2(c1_7__group_6,B,k7_group_4(c1_7__group_6,A,A)) = k12_group_2(c1_7__group_6,A,B)
            & k4_group_2(c1_7__group_6,B,k7_group_4(c1_7__group_6,A,A)) = k13_group_2(c1_7__group_6,A,B)
            & k11_group_2(c1_7__group_6,A,k13_group_2(c1_7__group_6,A,B)) = k13_group_2(c1_7__group_6,A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_7__group_6])],[i2_7_tmp__group_6,dh_c2_7__group_6]),
    [interesting(0.8),file(group_6,i1_7__group_6),[file(group_6,i1_7__group_6)]]).

fof(i1_7_tmp__group_6,plain,
    ( ( ~ v3_struct_0(c1_7__group_6)
      & v3_group_1(c1_7__group_6)
      & v4_group_1(c1_7__group_6)
      & l1_group_1(c1_7__group_6) )
   => ! [A] : 
        ( m1_group_2(A,c1_7__group_6)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_7__group_6))
           => ( k10_group_2(c1_7__group_6,A,k12_group_2(c1_7__group_6,A,B)) = k12_group_2(c1_7__group_6,A,B)
              & k3_group_2(c1_7__group_6,B,k7_group_4(c1_7__group_6,A,A)) = k12_group_2(c1_7__group_6,A,B)
              & k4_group_2(c1_7__group_6,B,k7_group_4(c1_7__group_6,A,A)) = k13_group_2(c1_7__group_6,A,B)
              & k11_group_2(c1_7__group_6,A,k13_group_2(c1_7__group_6,A,B)) = k13_group_2(c1_7__group_6,A,B) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__group_6])],[dt_c1_7__group_6,i1_7__group_6]),
    [interesting(1),t6_group_6]).

fof(t6_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k10_group_2(A,B,k12_group_2(A,B,C)) = k12_group_2(A,B,C)
                & k3_group_2(A,C,k7_group_4(A,B,B)) = k12_group_2(A,B,C)
                & k4_group_2(A,C,k7_group_4(A,B,B)) = k13_group_2(A,B,C)
                & k11_group_2(A,B,k13_group_2(A,B,C)) = k13_group_2(A,B,C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__group_6,dh_c1_7__group_6]),
    [interesting(1),file(group_6,t6_group_6),[file(group_6,t6_group_6)]]).