% Mizar ND problem: t3_group_6,group_6,115,55 
fof(dh_c1_5__group_6,definition,
    ( ( ( ~ v3_struct_0(c1_5__group_6)
        & v3_group_1(c1_5__group_6)
        & v4_group_1(c1_5__group_6)
        & l1_group_1(c1_5__group_6) )
     => ! [A] : 
          ( m1_group_2(A,c1_5__group_6)
         => ! [B] : 
              ( m1_group_6(B,c1_5__group_6,A)
             => ! [C] : 
                  ( m1_group_6(C,c1_5__group_6,A)
                 => k9_group_2(c1_5__group_6,B,C) = k9_group_2(A,B,C) ) ) ) )
   => ! [D] : 
        ( ( ~ v3_struct_0(D)
          & v3_group_1(D)
          & v4_group_1(D)
          & l1_group_1(D) )
       => ! [E] : 
            ( m1_group_2(E,D)
           => ! [F] : 
                ( m1_group_6(F,D,E)
               => ! [G] : 
                    ( m1_group_6(G,D,E)
                   => k9_group_2(D,F,G) = k9_group_2(E,F,G) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_5__group_6),file(group_6,c1_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c1_5__group_6)]).

fof(dh_c2_5__group_6,definition,
    ( ( m1_group_2(c2_5__group_6,c1_5__group_6)
     => ! [A] : 
          ( m1_group_6(A,c1_5__group_6,c2_5__group_6)
         => ! [B] : 
              ( m1_group_6(B,c1_5__group_6,c2_5__group_6)
             => k9_group_2(c1_5__group_6,A,B) = k9_group_2(c2_5__group_6,A,B) ) ) )
   => ! [C] : 
        ( m1_group_2(C,c1_5__group_6)
       => ! [D] : 
            ( m1_group_6(D,c1_5__group_6,C)
           => ! [E] : 
                ( m1_group_6(E,c1_5__group_6,C)
               => k9_group_2(c1_5__group_6,D,E) = k9_group_2(C,D,E) ) ) ) ),
    introduced(definition,[new_symbol(c2_5__group_6),file(group_6,c2_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c2_5__group_6)]).

fof(dh_c3_5__group_6,definition,
    ( ( m1_group_6(c3_5__group_6,c1_5__group_6,c2_5__group_6)
     => ! [A] : 
          ( m1_group_6(A,c1_5__group_6,c2_5__group_6)
         => k9_group_2(c1_5__group_6,c3_5__group_6,A) = k9_group_2(c2_5__group_6,c3_5__group_6,A) ) )
   => ! [B] : 
        ( m1_group_6(B,c1_5__group_6,c2_5__group_6)
       => ! [C] : 
            ( m1_group_6(C,c1_5__group_6,c2_5__group_6)
           => k9_group_2(c1_5__group_6,B,C) = k9_group_2(c2_5__group_6,B,C) ) ) ),
    introduced(definition,[new_symbol(c3_5__group_6),file(group_6,c3_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c3_5__group_6)]).

fof(dh_c4_5__group_6,definition,
    ( ( m1_group_6(c4_5__group_6,c1_5__group_6,c2_5__group_6)
     => k9_group_2(c1_5__group_6,c3_5__group_6,c4_5__group_6) = k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6) )
   => ! [A] : 
        ( m1_group_6(A,c1_5__group_6,c2_5__group_6)
       => k9_group_2(c1_5__group_6,c3_5__group_6,A) = k9_group_2(c2_5__group_6,c3_5__group_6,A) ) ),
    introduced(definition,[new_symbol(c4_5__group_6),file(group_6,c4_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c4_5__group_6)]).

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

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

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

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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

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

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

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

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

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

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_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_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(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(fc1_group_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g1_group_1(A,B))
        & v1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,fc1_group_1),
    [interesting(0.9),axiom,file(group_1,fc1_group_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(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(free_g1_group_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] : 
          ( g1_group_1(A,B) = g1_group_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(group_1,g1_group_1),
    [interesting(0.9),axiom,file(group_1,g1_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(dt_g1_group_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_group_1(g1_group_1(A,B))
        & l1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,g1_group_1),
    [interesting(0.9),axiom,file(group_1,g1_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_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(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_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)
          & ~ v3_struct_0(B)
          & v1_group_1(B)
          & v2_group_1(B)
          & v3_group_1(B)
          & v4_group_1(B) ) ) ),
    file(group_2,rc1_group_2),
    [interesting(0.9),axiom,file(group_2,rc1_group_2)]).

fof(rc3_group_1,theorem,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A)
      & v2_group_1(A)
      & v3_group_1(A)
      & v4_group_1(A) ) ),
    file(group_1,rc3_group_1),
    [interesting(0.9),axiom,file(group_1,rc3_group_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(abstractness_v1_group_1,theorem,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_group_1(A)
       => A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ),
    file(group_1,v1_group_1),
    [interesting(0.9),axiom,file(group_1,v1_group_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_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_group_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ? [C] : m1_group_6(C,A,B) ) ),
    file(group_6,m1_group_6),
    [interesting(0.9),axiom,file(group_6,m1_group_6)]).

fof(redefinition_m1_group_6,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ! [C] : 
          ( m1_group_6(C,A,B)
        <=> m1_group_2(C,B) ) ) ),
    file(group_6,m1_group_6),
    [interesting(0.9),axiom,file(group_6,m1_group_6)]).

fof(dt_k8_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_group_2(C,A) )
     => ( v1_group_1(k8_group_2(A,B,C))
        & m1_group_2(k8_group_2(A,B,C),A) ) ) ),
    file(group_2,k8_group_2),
    [interesting(0.9),axiom,file(group_2,k8_group_2)]).

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_group_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ! [C] : 
          ( m1_group_6(C,A,B)
         => m1_group_2(C,A) ) ) ),
    file(group_6,m1_group_6),
    [interesting(0.9),axiom,file(group_6,m1_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(rc1_group_1,theorem,(
    ? [A] : 
      ( l1_group_1(A)
      & v1_group_1(A) ) ),
    file(group_1,rc1_group_1),
    [interesting(0.9),axiom,file(group_1,rc1_group_1)]).

fof(rc2_group_1,theorem,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A) ) ),
    file(group_1,rc2_group_1),
    [interesting(0.9),axiom,file(group_1,rc2_group_1)]).

fof(commutativity_k9_group_2,theorem,(
    ! [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) )
     => k9_group_2(A,B,C) = k9_group_2(A,C,B) ) ),
    file(group_2,k9_group_2),
    [interesting(0.9),axiom,file(group_2,k9_group_2)]).

fof(redefinition_k9_group_2,definition,(
    ! [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) )
     => k9_group_2(A,B,C) = k8_group_2(A,B,C) ) ),
    file(group_2,k9_group_2),
    [interesting(0.9),axiom,file(group_2,k9_group_2)]).

fof(dt_k9_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_group_2(C,A) )
     => ( v1_group_1(k9_group_2(A,B,C))
        & m1_group_2(k9_group_2(A,B,C),A) ) ) ),
    file(group_2,k9_group_2),
    [interesting(0.9),axiom,file(group_2,k9_group_2)]).

fof(dt_c1_5__group_6,assumption,
    ( ~ v3_struct_0(c1_5__group_6)
    & v3_group_1(c1_5__group_6)
    & v4_group_1(c1_5__group_6)
    & l1_group_1(c1_5__group_6) ),
    introduced(assumption,[file(group_6,c1_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c1_5__group_6)]).

fof(dt_c2_5__group_6,assumption,(
    m1_group_2(c2_5__group_6,c1_5__group_6) ),
    introduced(assumption,[file(group_6,c2_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c2_5__group_6)]).

fof(dt_c3_5__group_6,assumption,(
    m1_group_6(c3_5__group_6,c1_5__group_6,c2_5__group_6) ),
    introduced(assumption,[file(group_6,c3_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c3_5__group_6)]).

fof(dt_c4_5__group_6,assumption,(
    m1_group_6(c4_5__group_6,c1_5__group_6,c2_5__group_6) ),
    introduced(assumption,[file(group_6,c4_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c4_5__group_6)]).

fof(de_c5_5__group_6,definition,(
    c5_5__group_6 = k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6) ),
    introduced(definition,[new_symbol(c5_5__group_6),file(group_6,c5_5__group_6)]),
    [interesting(0.8),axiom,file(group_6,c5_5__group_6)]).

fof(t65_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ( ( m1_group_2(A,B)
                  & m1_group_2(B,C) )
               => m1_group_2(A,C) ) ) ) ) ),
    file(group_2,t65_group_2),
    [interesting(0.9),axiom,file(group_2,t65_group_2)]).

fof(e2_5__group_6,plain,(
    m1_group_2(k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6),c1_5__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6])],[reflexivity_r1_tarski,rc1_funct_2,rc2_partfun1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,free_g1_group_1,dt_g1_group_1,dt_u1_group_1,dt_u1_struct_0,fc1_struct_0,abstractness_v1_group_1,existence_l1_struct_0,existence_m1_group_6,redefinition_m1_group_6,dt_k8_group_2,dt_l1_struct_0,dt_m1_group_6,rc1_group_1,rc1_group_2,rc2_group_1,rc3_group_1,rc3_struct_0,commutativity_k9_group_2,existence_l1_group_1,existence_m1_group_2,redefinition_k9_group_2,dt_k9_group_2,dt_l1_group_1,dt_m1_group_2,dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6,cc1_group_1,cc1_group_2,t65_group_2]),
    [interesting(0.8),file(group_6,e2_5__group_6),[file(group_6,e2_5__group_6)]]).

fof(dt_c5_5__group_6,plain,(
    m1_group_2(c5_5__group_6,c1_5__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6])],[reflexivity_r1_tarski,rc1_funct_2,rc2_partfun1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,free_g1_group_1,existence_l1_struct_0,dt_g1_group_1,dt_l1_struct_0,dt_u1_group_1,dt_u1_struct_0,fc1_struct_0,rc1_group_2,rc3_group_1,rc3_struct_0,abstractness_v1_group_1,existence_l1_group_1,existence_m1_group_6,redefinition_m1_group_6,dt_k8_group_2,dt_l1_group_1,dt_m1_group_6,cc1_group_1,cc1_group_2,rc1_group_1,rc2_group_1,commutativity_k9_group_2,existence_m1_group_2,redefinition_k9_group_2,dt_k9_group_2,dt_m1_group_2,dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6,de_c5_5__group_6,e2_5__group_6]),
    [interesting(0.8),file(group_6,c5_5__group_6),[file(group_6,c5_5__group_6)]]).

fof(fc10_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc10_finset_1)]).

fof(fc11_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc11_finset_1)]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(commutativity_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(idempotence_k5_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(symmetry_r1_group_2,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
       => r1_group_2(A,C,B) ) ) ),
    file(group_2,r1_group_2),
    [interesting(0.9),axiom,file(group_2,r1_group_2)]).

fof(reflexivity_r1_group_2,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => r1_group_2(A,B,B) ) ),
    file(group_2,r1_group_2),
    [interesting(0.9),axiom,file(group_2,r1_group_2)]).

fof(redefinition_k5_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_1)]).

fof(redefinition_r1_group_2,definition,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
      <=> B = C ) ) ),
    file(group_2,r1_group_2),
    [interesting(0.9),axiom,file(group_2,r1_group_2)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    [interesting(0.9),axiom,file(subset_1,k5_subset_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(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(commutativity_k3_finsub_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_finsub_1(A,B,C) = k3_finsub_1(A,C,B) ) ),
    file(finsub_1,k3_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,k3_finsub_1)]).

fof(idempotence_k3_finsub_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_finsub_1(A,B,B) = B ) ),
    file(finsub_1,k3_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,k3_finsub_1)]).

fof(redefinition_k3_finsub_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_finsub_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(finsub_1,k3_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,k3_finsub_1)]).

fof(dt_k3_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k3_finsub_1(A,B,C),A) ) ),
    file(finsub_1,k3_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,k3_finsub_1)]).

fof(d10_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_group_2(C,A)
             => ! [D] : 
                  ( ( v1_group_1(D)
                    & m1_group_2(D,A) )
                 => ( D = k8_group_2(A,B,C)
                  <=> u1_struct_0(D) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ) ) ),
    file(group_2,d10_group_2),
    [interesting(0.9),axiom,file(group_2,d10_group_2)]).

fof(e1_5__group_6,plain,
    ( u1_struct_0(k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6)) = k5_subset_1(u1_struct_0(c2_5__group_6),k7_group_2(c2_5__group_6,c3_5__group_6),k7_group_2(c2_5__group_6,c4_5__group_6))
    & u1_struct_0(k9_group_2(c1_5__group_6,c3_5__group_6,c4_5__group_6)) = k5_subset_1(u1_struct_0(c1_5__group_6),k7_group_2(c1_5__group_6,c3_5__group_6),k7_group_2(c1_5__group_6,c4_5__group_6))
    & k7_group_2(c2_5__group_6,c3_5__group_6) = u1_struct_0(c3_5__group_6)
    & u1_struct_0(c4_5__group_6) = k7_group_2(c2_5__group_6,c4_5__group_6)
    & k7_group_2(c1_5__group_6,c3_5__group_6) = u1_struct_0(c3_5__group_6)
    & u1_struct_0(c4_5__group_6) = k7_group_2(c1_5__group_6,c4_5__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6])],[cc1_funct_2,rc1_funct_2,rc2_partfun1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc1_group_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t2_boole,t4_subset,t5_subset,free_g1_group_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,existence_l1_struct_0,existence_m1_group_6,existence_m1_subset_1,redefinition_m1_group_6,dt_g1_group_1,dt_k3_xboole_0,dt_l1_struct_0,dt_m1_group_6,dt_m1_subset_1,dt_u1_group_1,cc1_finset_1,fc1_struct_0,rc1_group_2,rc1_xboole_0,rc2_xboole_0,rc3_group_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_finsub_1,idempotence_k3_finsub_1,commutativity_k5_subset_1,idempotence_k5_subset_1,commutativity_k9_group_2,abstractness_v1_group_1,existence_l1_group_1,existence_m1_group_2,redefinition_k3_finsub_1,redefinition_k5_subset_1,redefinition_k9_group_2,dt_k1_zfmisc_1,dt_k3_finsub_1,dt_k5_subset_1,dt_k7_group_2,dt_k8_group_2,dt_k9_group_2,dt_l1_group_1,dt_m1_group_2,dt_u1_struct_0,dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6,cc1_group_1,cc1_group_2,rc1_group_1,rc2_group_1,d9_group_2,d10_group_2]),
    [interesting(0.8),file(group_6,e1_5__group_6),[file(group_6,e1_5__group_6)]]).

fof(t97_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)
         => ! [C] : 
              ( m1_group_2(C,A)
             => ( ! [D] : 
                    ( m1_group_2(D,A)
                   => ( D = k8_group_2(A,B,C)
                     => u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) )
                & ! [D] : 
                    ( ( v1_group_1(D)
                      & m1_group_2(D,A) )
                   => ( u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C))
                     => r1_group_2(A,D,k8_group_2(A,B,C)) ) ) ) ) ) ) ),
    file(group_2,t97_group_2),
    [interesting(0.9),axiom,file(group_2,t97_group_2)]).

fof(e3_5__group_6,plain,(
    k9_group_2(c1_5__group_6,c3_5__group_6,c4_5__group_6) = c5_5__group_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,cc2_finset_1,fc10_finset_1,fc11_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,free_g1_group_1,existence_l1_struct_0,existence_m1_group_6,existence_m1_subset_1,redefinition_m1_group_6,dt_g1_group_1,dt_k1_zfmisc_1,dt_l1_struct_0,dt_m1_group_6,dt_m1_subset_1,dt_u1_group_1,fc1_struct_0,rc1_group_2,rc3_group_1,rc3_struct_0,t3_subset,commutativity_k3_xboole_0,idempotence_k3_xboole_0,commutativity_k5_subset_1,idempotence_k5_subset_1,commutativity_k9_group_2,symmetry_r1_group_2,reflexivity_r1_group_2,abstractness_v1_group_1,existence_l1_group_1,existence_m1_group_2,redefinition_k5_subset_1,redefinition_k9_group_2,redefinition_r1_group_2,dt_k3_xboole_0,dt_k5_subset_1,dt_k7_group_2,dt_k8_group_2,dt_k9_group_2,dt_l1_group_1,dt_m1_group_2,dt_u1_struct_0,dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6,dt_c5_5__group_6,de_c5_5__group_6,cc1_group_1,cc1_group_2,rc1_group_1,rc2_group_1,d9_group_2,e1_5__group_6,t97_group_2]),
    [interesting(0.8),file(group_6,e3_5__group_6),[file(group_6,e3_5__group_6)]]).

fof(e4_5__group_6,plain,(
    k9_group_2(c1_5__group_6,c3_5__group_6,c4_5__group_6) = k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6])],[reflexivity_r1_tarski,rc1_funct_2,rc2_partfun1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,free_g1_group_1,existence_l1_struct_0,dt_g1_group_1,dt_l1_struct_0,dt_u1_group_1,dt_u1_struct_0,fc1_struct_0,rc1_group_2,rc3_group_1,rc3_struct_0,abstractness_v1_group_1,existence_l1_group_1,existence_m1_group_2,existence_m1_group_6,redefinition_m1_group_6,dt_k8_group_2,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,cc1_group_1,cc1_group_2,rc1_group_1,rc2_group_1,commutativity_k9_group_2,redefinition_k9_group_2,dt_k9_group_2,dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6,dt_c5_5__group_6,de_c5_5__group_6,e3_5__group_6]),
    [interesting(0.8),file(group_6,e4_5__group_6),[file(group_6,e4_5__group_6)]]).

fof(i4_5__group_6,theorem,(
    $true ),
    introduced(tautology,[file(group_6,i4_5__group_6)]),
    [interesting(0.8),trivial,file(group_6,i4_5__group_6)]).

fof(i3_5__group_6,plain,(
    k9_group_2(c1_5__group_6,c3_5__group_6,c4_5__group_6) = k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6,dt_c3_5__group_6,dt_c4_5__group_6])],[e4_5__group_6,i4_5__group_6]),
    [interesting(0.8),file(group_6,i3_5__group_6),[file(group_6,i3_5__group_6)]]).

fof(i3_5_tmp__group_6,plain,
    ( ( m1_group_6(c3_5__group_6,c1_5__group_6,c2_5__group_6)
      & m1_group_6(c4_5__group_6,c1_5__group_6,c2_5__group_6) )
   => k9_group_2(c1_5__group_6,c3_5__group_6,c4_5__group_6) = k9_group_2(c2_5__group_6,c3_5__group_6,c4_5__group_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6]),discharge_asm(discharge,[dt_c3_5__group_6,dt_c4_5__group_6])],[dt_c3_5__group_6,dt_c4_5__group_6,i3_5__group_6]),
    [interesting(0.8),i2_5__group_6]).

fof(i2_5__group_6,plain,(
    ! [A] : 
      ( m1_group_6(A,c1_5__group_6,c2_5__group_6)
     => ! [B] : 
          ( m1_group_6(B,c1_5__group_6,c2_5__group_6)
         => k9_group_2(c1_5__group_6,A,B) = k9_group_2(c2_5__group_6,A,B) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__group_6,dt_c2_5__group_6])],[i3_5_tmp__group_6,dh_c3_5__group_6,dh_c4_5__group_6]),
    [interesting(0.8),file(group_6,i2_5__group_6),[file(group_6,i2_5__group_6)]]).

fof(i2_5_tmp__group_6,plain,
    ( m1_group_2(c2_5__group_6,c1_5__group_6)
   => ! [A] : 
        ( m1_group_6(A,c1_5__group_6,c2_5__group_6)
       => ! [B] : 
            ( m1_group_6(B,c1_5__group_6,c2_5__group_6)
           => k9_group_2(c1_5__group_6,A,B) = k9_group_2(c2_5__group_6,A,B) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__group_6]),discharge_asm(discharge,[dt_c2_5__group_6])],[dt_c2_5__group_6,i2_5__group_6]),
    [interesting(0.8),i1_5__group_6]).

fof(i1_5__group_6,plain,(
    ! [A] : 
      ( m1_group_2(A,c1_5__group_6)
     => ! [B] : 
          ( m1_group_6(B,c1_5__group_6,A)
         => ! [C] : 
              ( m1_group_6(C,c1_5__group_6,A)
             => k9_group_2(c1_5__group_6,B,C) = k9_group_2(A,B,C) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__group_6])],[i2_5_tmp__group_6,dh_c2_5__group_6]),
    [interesting(0.8),file(group_6,i1_5__group_6),[file(group_6,i1_5__group_6)]]).

fof(i1_5_tmp__group_6,plain,
    ( ( ~ v3_struct_0(c1_5__group_6)
      & v3_group_1(c1_5__group_6)
      & v4_group_1(c1_5__group_6)
      & l1_group_1(c1_5__group_6) )
   => ! [A] : 
        ( m1_group_2(A,c1_5__group_6)
       => ! [B] : 
            ( m1_group_6(B,c1_5__group_6,A)
           => ! [C] : 
                ( m1_group_6(C,c1_5__group_6,A)
               => k9_group_2(c1_5__group_6,B,C) = k9_group_2(A,B,C) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__group_6])],[dt_c1_5__group_6,i1_5__group_6]),
    [interesting(1),t3_group_6]).

fof(t3_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_group_6(C,A,B)
             => ! [D] : 
                  ( m1_group_6(D,A,B)
                 => k9_group_2(A,C,D) = k9_group_2(B,C,D) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__group_6,dh_c1_5__group_6]),
    [interesting(1),file(group_6,t3_group_6),[file(group_6,t3_group_6)]]).