% Mizar ND problem: t1_group_6,group_6,35,55 
fof(dh_c1_1__group_6,definition,
    ( ( ~ v1_xboole_0(c1_1__group_6)
     => ! [A] : 
          ( ~ v1_xboole_0(A)
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,c1_1__group_6,A)
                & m2_relset_1(B,c1_1__group_6,A) )
             => ( v2_funct_1(B)
              <=> ! [C] : 
                    ( m1_subset_1(C,c1_1__group_6)
                   => ! [D] : 
                        ( m1_subset_1(D,c1_1__group_6)
                       => ( k8_funct_2(c1_1__group_6,A,B,C) = k8_funct_2(c1_1__group_6,A,B,D)
                         => C = D ) ) ) ) ) ) )
   => ! [E] : 
        ( ~ v1_xboole_0(E)
       => ! [F] : 
            ( ~ v1_xboole_0(F)
           => ! [G] : 
                ( ( v1_funct_1(G)
                  & v1_funct_2(G,E,F)
                  & m2_relset_1(G,E,F) )
               => ( v2_funct_1(G)
                <=> ! [H] : 
                      ( m1_subset_1(H,E)
                     => ! [I] : 
                          ( m1_subset_1(I,E)
                         => ( k8_funct_2(E,F,G,H) = k8_funct_2(E,F,G,I)
                           => H = I ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__group_6),file(group_6,c1_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,c1_1__group_6)]).

fof(dh_c2_1__group_6,definition,
    ( ( ~ v1_xboole_0(c2_1__group_6)
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,c1_1__group_6,c2_1__group_6)
            & m2_relset_1(A,c1_1__group_6,c2_1__group_6) )
         => ( v2_funct_1(A)
          <=> ! [B] : 
                ( m1_subset_1(B,c1_1__group_6)
               => ! [C] : 
                    ( m1_subset_1(C,c1_1__group_6)
                   => ( k8_funct_2(c1_1__group_6,c2_1__group_6,A,B) = k8_funct_2(c1_1__group_6,c2_1__group_6,A,C)
                     => B = C ) ) ) ) ) )
   => ! [D] : 
        ( ~ v1_xboole_0(D)
       => ! [E] : 
            ( ( v1_funct_1(E)
              & v1_funct_2(E,c1_1__group_6,D)
              & m2_relset_1(E,c1_1__group_6,D) )
           => ( v2_funct_1(E)
            <=> ! [F] : 
                  ( m1_subset_1(F,c1_1__group_6)
                 => ! [G] : 
                      ( m1_subset_1(G,c1_1__group_6)
                     => ( k8_funct_2(c1_1__group_6,D,E,F) = k8_funct_2(c1_1__group_6,D,E,G)
                       => F = G ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__group_6),file(group_6,c2_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,c2_1__group_6)]).

fof(dh_c3_1__group_6,definition,
    ( ( ( v1_funct_1(c3_1__group_6)
        & v1_funct_2(c3_1__group_6,c1_1__group_6,c2_1__group_6)
        & m2_relset_1(c3_1__group_6,c1_1__group_6,c2_1__group_6) )
     => ( v2_funct_1(c3_1__group_6)
      <=> ! [A] : 
            ( m1_subset_1(A,c1_1__group_6)
           => ! [B] : 
                ( m1_subset_1(B,c1_1__group_6)
               => ( k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,A) = k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,B)
                 => A = B ) ) ) ) )
   => ! [C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,c1_1__group_6,c2_1__group_6)
          & m2_relset_1(C,c1_1__group_6,c2_1__group_6) )
       => ( v2_funct_1(C)
        <=> ! [D] : 
              ( m1_subset_1(D,c1_1__group_6)
             => ! [E] : 
                  ( m1_subset_1(E,c1_1__group_6)
                 => ( k8_funct_2(c1_1__group_6,c2_1__group_6,C,D) = k8_funct_2(c1_1__group_6,c2_1__group_6,C,E)
                   => D = E ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_1__group_6),file(group_6,c3_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,c3_1__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(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(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(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(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(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_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(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_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(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(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

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_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(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(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(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(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(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_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

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_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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_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_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_c1_1__group_6,assumption,(
    ~ v1_xboole_0(c1_1__group_6) ),
    introduced(assumption,[file(group_6,c1_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,c1_1__group_6)]).

fof(dt_c2_1__group_6,assumption,(
    ~ v1_xboole_0(c2_1__group_6) ),
    introduced(assumption,[file(group_6,c2_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,c2_1__group_6)]).

fof(dt_c3_1__group_6,assumption,
    ( v1_funct_1(c3_1__group_6)
    & v1_funct_2(c3_1__group_6,c1_1__group_6,c2_1__group_6)
    & m2_relset_1(c3_1__group_6,c1_1__group_6,c2_1__group_6) ),
    introduced(assumption,[file(group_6,c3_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,c3_1__group_6)]).

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(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(t25_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => ( v2_funct_1(C)
        <=> ! [D,E] : 
              ( ( r2_hidden(D,A)
                & r2_hidden(E,A)
                & k1_funct_1(C,D) = k1_funct_1(C,E) )
             => D = E ) ) ) ) ),
    file(funct_2,t25_funct_2),
    [interesting(0.9),axiom,file(funct_2,t25_funct_2)]).

fof(e1_1__group_6,plain,
    ( v2_funct_1(c3_1__group_6)
   => ! [A] : 
        ( m1_subset_1(A,c1_1__group_6)
       => ! [B] : 
            ( m1_subset_1(B,c1_1__group_6)
           => ( k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,A) = k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,B)
             => A = B ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6])],[reflexivity_r1_tarski,cc1_funct_2,cc2_finset_1,fc14_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,rc1_funct_2,rc1_partfun1,rc1_xboole_0,rc2_partfun1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_relset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k8_funct_2,dt_m1_subset_1,dt_m2_relset_1,dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6,fc1_xboole_0,t1_subset,t6_boole,t7_boole,t25_funct_2]),
    [interesting(0.8),file(group_6,e1_1__group_6),[file(group_6,e1_1__group_6)]]).

fof(e2_1__group_6,assumption,(
    ! [A] : 
      ( m1_subset_1(A,c1_1__group_6)
     => ! [B] : 
          ( m1_subset_1(B,c1_1__group_6)
         => ( k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,A) = k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,B)
           => A = B ) ) ) ),
    introduced(assumption,[file(group_6,e2_1__group_6)]),
    [interesting(0.8),axiom,file(group_6,e2_1__group_6)]).

fof(e3_1__group_6,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,c1_1__group_6)
        & r2_hidden(B,c1_1__group_6)
        & k1_funct_1(c3_1__group_6,A) = k1_funct_1(c3_1__group_6,B) )
     => A = B ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6,e2_1__group_6])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_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,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc5_funct_2,cc6_funct_2,rc1_funct_2,rc1_xboole_0,rc2_partfun1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k8_funct_2,dt_k1_funct_1,dt_k8_funct_2,dt_m1_subset_1,dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6,t1_subset,t7_boole,e2_1__group_6]),
    [interesting(0.8),file(group_6,e3_1__group_6),[file(group_6,e3_1__group_6)]]).

fof(e4_1__group_6,plain,(
    v2_funct_1(c3_1__group_6) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6,e2_1__group_6])],[reflexivity_r1_tarski,cc1_funct_2,cc2_finset_1,fc14_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,dt_c2_1__group_6,cc1_finset_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,rc1_funct_2,rc1_partfun1,rc1_xboole_0,rc2_partfun1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_m2_relset_1,dt_c1_1__group_6,dt_c3_1__group_6,fc1_xboole_0,t1_subset,t6_boole,t7_boole,e3_1__group_6,t25_funct_2]),
    [interesting(0.8),file(group_6,e4_1__group_6),[file(group_6,e4_1__group_6)]]).

fof(i5_1__group_6,theorem,(
    $true ),
    introduced(tautology,[file(group_6,i5_1__group_6)]),
    [interesting(0.8),trivial,file(group_6,i5_1__group_6)]).

fof(i4_1__group_6,plain,(
    v2_funct_1(c3_1__group_6) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6,e2_1__group_6])],[e4_1__group_6,i5_1__group_6]),
    [interesting(0.8),file(group_6,i4_1__group_6),[file(group_6,i4_1__group_6)]]).

fof(i3_1__group_6,plain,
    ( ! [A] : 
        ( m1_subset_1(A,c1_1__group_6)
       => ! [B] : 
            ( m1_subset_1(B,c1_1__group_6)
           => ( k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,A) = k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,B)
             => A = B ) ) )
   => v2_funct_1(c3_1__group_6) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6]),discharge_asm(discharge,[e2_1__group_6])],[e2_1__group_6,i4_1__group_6]),
    [interesting(0.8),file(group_6,i3_1__group_6),[file(group_6,i3_1__group_6)]]).

fof(i2_1__group_6,plain,
    ( v2_funct_1(c3_1__group_6)
  <=> ! [A] : 
        ( m1_subset_1(A,c1_1__group_6)
       => ! [B] : 
            ( m1_subset_1(B,c1_1__group_6)
           => ( k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,A) = k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,B)
             => A = B ) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6,dt_c3_1__group_6])],[e1_1__group_6,i3_1__group_6]),
    [interesting(0.8),file(group_6,i2_1__group_6),[file(group_6,i2_1__group_6)]]).

fof(i2_1_tmp__group_6,plain,
    ( ( v1_funct_1(c3_1__group_6)
      & v1_funct_2(c3_1__group_6,c1_1__group_6,c2_1__group_6)
      & m2_relset_1(c3_1__group_6,c1_1__group_6,c2_1__group_6) )
   => ( v2_funct_1(c3_1__group_6)
    <=> ! [A] : 
          ( m1_subset_1(A,c1_1__group_6)
         => ! [B] : 
              ( m1_subset_1(B,c1_1__group_6)
             => ( k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,A) = k8_funct_2(c1_1__group_6,c2_1__group_6,c3_1__group_6,B)
               => A = B ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6]),discharge_asm(discharge,[dt_c3_1__group_6])],[dt_c3_1__group_6,i2_1__group_6]),
    [interesting(0.8),i1_1__group_6]).

fof(i1_1__group_6,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,c1_1__group_6,c2_1__group_6)
        & m2_relset_1(A,c1_1__group_6,c2_1__group_6) )
     => ( v2_funct_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,c1_1__group_6)
           => ! [C] : 
                ( m1_subset_1(C,c1_1__group_6)
               => ( k8_funct_2(c1_1__group_6,c2_1__group_6,A,B) = k8_funct_2(c1_1__group_6,c2_1__group_6,A,C)
                 => B = C ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__group_6,dt_c2_1__group_6])],[i2_1_tmp__group_6,dh_c3_1__group_6]),
    [interesting(0.8),file(group_6,i1_1__group_6),[file(group_6,i1_1__group_6)]]).

fof(i1_1_tmp__group_6,plain,
    ( ( ~ v1_xboole_0(c1_1__group_6)
      & ~ v1_xboole_0(c2_1__group_6) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,c1_1__group_6,c2_1__group_6)
          & m2_relset_1(A,c1_1__group_6,c2_1__group_6) )
       => ( v2_funct_1(A)
        <=> ! [B] : 
              ( m1_subset_1(B,c1_1__group_6)
             => ! [C] : 
                  ( m1_subset_1(C,c1_1__group_6)
                 => ( k8_funct_2(c1_1__group_6,c2_1__group_6,A,B) = k8_funct_2(c1_1__group_6,c2_1__group_6,A,C)
                   => B = C ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__group_6,dt_c2_1__group_6])],[dt_c1_1__group_6,dt_c2_1__group_6,i1_1__group_6]),
    [interesting(1),t1_group_6]).

fof(t1_group_6,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_funct_1(C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ( k8_funct_2(A,B,C,D) = k8_funct_2(A,B,C,E)
                         => D = E ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__group_6,dh_c1_1__group_6,dh_c2_1__group_6]),
    [interesting(1),file(group_6,t1_group_6),[file(group_6,t1_group_6)]]).