% Mizar ND problem: t7_arytm_1,arytm_1,100,26 
fof(dh_c1_8__arytm_1,definition,
    ( ( m1_subset_1(c1_8__arytm_1,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ! [B] : 
              ( m1_subset_1(B,k2_arytm_2)
             => ( r1_arytm_2(c1_8__arytm_1,A)
              <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,B),k7_arytm_2(A,B)) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,k2_arytm_2)
       => ! [D] : 
            ( m1_subset_1(D,k2_arytm_2)
           => ! [E] : 
                ( m1_subset_1(E,k2_arytm_2)
               => ( r1_arytm_2(C,D)
                <=> r1_arytm_2(k7_arytm_2(C,E),k7_arytm_2(D,E)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_8__arytm_1),file(arytm_1,c1_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c1_8__arytm_1)]).

fof(dh_c2_8__arytm_1,definition,
    ( ( m1_subset_1(c2_8__arytm_1,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
          <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,A),k7_arytm_2(c2_8__arytm_1,A)) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k2_arytm_2)
       => ! [C] : 
            ( m1_subset_1(C,k2_arytm_2)
           => ( r1_arytm_2(c1_8__arytm_1,B)
            <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,C),k7_arytm_2(B,C)) ) ) ) ),
    introduced(definition,[new_symbol(c2_8__arytm_1),file(arytm_1,c2_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c2_8__arytm_1)]).

fof(dh_c3_8__arytm_1,definition,
    ( ( m1_subset_1(c3_8__arytm_1,k2_arytm_2)
     => ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
      <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ) )
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
        <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,A),k7_arytm_2(c2_8__arytm_1,A)) ) ) ),
    introduced(definition,[new_symbol(c3_8__arytm_1),file(arytm_1,c3_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c3_8__arytm_1)]).

fof(e1_8_1__arytm_1,assumption,(
    r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1) ),
    introduced(assumption,[file(arytm_1,e1_8_1__arytm_1)]),
    [interesting(0.65),axiom,file(arytm_1,e1_8_1__arytm_1)]).

fof(commutativity_k7_arytm_2,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => k7_arytm_2(A,B) = k7_arytm_2(B,A) ) ),
    file(arytm_2,k7_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,k7_arytm_2)]).

fof(connectedness_r1_arytm_2,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => ( r1_arytm_2(A,B)
        | r1_arytm_2(B,A) ) ) ),
    file(arytm_2,r1_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,r1_arytm_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_k2_arytm_2,axiom,(
    $true ),
    file(arytm_2,k2_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,k2_arytm_2)]).

fof(dt_k7_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => m1_subset_1(k7_arytm_2(A,B),k2_arytm_2) ) ),
    file(arytm_2,k7_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,k7_arytm_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_c1_8__arytm_1,assumption,(
    m1_subset_1(c1_8__arytm_1,k2_arytm_2) ),
    introduced(assumption,[file(arytm_1,c1_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c1_8__arytm_1)]).

fof(dh_c1_8_1__arytm_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & k7_arytm_2(c1_8__arytm_1,A) = c2_8__arytm_1 )
   => ( m1_subset_1(c1_8_1__arytm_1,k2_arytm_2)
      & k7_arytm_2(c1_8__arytm_1,c1_8_1__arytm_1) = c2_8__arytm_1 ) ),
    introduced(definition,[new_symbol(c1_8_1__arytm_1),file(arytm_1,c1_8_1__arytm_1)]),
    [interesting(0.65),axiom,file(arytm_1,c1_8_1__arytm_1)]).

fof(dt_c2_8__arytm_1,assumption,(
    m1_subset_1(c2_8__arytm_1,k2_arytm_2) ),
    introduced(assumption,[file(arytm_1,c2_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c2_8__arytm_1)]).

fof(t10_arytm_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ~ ( r1_arytm_2(A,B)
              & ! [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                 => k7_arytm_2(A,C) != B ) ) ) ) ),
    file(arytm_2,t10_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t10_arytm_2)]).

fof(e2_8_1__arytm_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & k7_arytm_2(c1_8__arytm_1,A) = c2_8__arytm_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1])],[commutativity_k7_arytm_2,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1,t10_arytm_2]),
    [interesting(0.65),file(arytm_1,e2_8_1__arytm_1),[file(arytm_1,e2_8_1__arytm_1)]]).

fof(dt_c1_8_1__arytm_1,plain,(
    m1_subset_1(c1_8_1__arytm_1,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1])],[dh_c1_8_1__arytm_1,e2_8_1__arytm_1]),
    [interesting(0.65),file(arytm_1,c1_8_1__arytm_1),[file(arytm_1,c1_8_1__arytm_1)]]).

fof(dt_c3_8__arytm_1,assumption,(
    m1_subset_1(c3_8__arytm_1,k2_arytm_2) ),
    introduced(assumption,[file(arytm_1,c3_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c3_8__arytm_1)]).

fof(e3_8_1__arytm_1,plain,(
    k7_arytm_2(c1_8__arytm_1,c1_8_1__arytm_1) = c2_8__arytm_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1])],[dh_c1_8_1__arytm_1,e2_8_1__arytm_1]),
    [interesting(0.65),file(arytm_1,e3_8_1__arytm_1),[file(arytm_1,e3_8_1__arytm_1)]]).

fof(t7_arytm_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => k7_arytm_2(A,k7_arytm_2(B,C)) = k7_arytm_2(k7_arytm_2(A,B),C) ) ) ) ),
    file(arytm_2,t7_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t7_arytm_2)]).

fof(e4_8_1__arytm_1,plain,(
    k7_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),c1_8_1__arytm_1) = k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_8__arytm_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1])],[commutativity_k7_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c1_8_1__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e3_8_1__arytm_1,t7_arytm_2]),
    [interesting(0.65),file(arytm_1,e4_8_1__arytm_1),[file(arytm_1,e4_8_1__arytm_1)]]).

fof(t20_arytm_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( A = k7_arytm_2(B,C)
               => r1_arytm_2(C,A) ) ) ) ) ),
    file(arytm_2,t20_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t20_arytm_2)]).

fof(e5_8_1__arytm_1,plain,(
    r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_8__arytm_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1])],[commutativity_k7_arytm_2,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c1_8_1__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e4_8_1__arytm_1,t20_arytm_2]),
    [interesting(0.65),file(arytm_1,e5_8_1__arytm_1),[file(arytm_1,e5_8_1__arytm_1)]]).

fof(i2_8_1__arytm_1,theorem,(
    $true ),
    introduced(tautology,[file(arytm_1,i2_8_1__arytm_1)]),
    [interesting(0.65),trivial,file(arytm_1,i2_8_1__arytm_1)]).

fof(i1_8_1__arytm_1,plain,(
    r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_8__arytm_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,e1_8_1__arytm_1])],[e5_8_1__arytm_1,i2_8_1__arytm_1]),
    [interesting(0.65),file(arytm_1,i1_8_1__arytm_1),[file(arytm_1,i1_8_1__arytm_1)]]).

fof(e1_8__arytm_1,plain,
    ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
   => r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_8__arytm_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1]),discharge_asm(discharge,[e1_8_1__arytm_1])],[e1_8_1__arytm_1,i1_8_1__arytm_1]),
    [interesting(0.8),file(arytm_1,e1_8__arytm_1),[file(arytm_1,e1_8__arytm_1)]]).

fof(e2_8__arytm_1,assumption,(
    r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ),
    introduced(assumption,[file(arytm_1,e2_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,e2_8__arytm_1)]).

fof(dh_c4_8__arytm_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & k7_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),A) = k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1) )
   => ( m1_subset_1(c4_8__arytm_1,k2_arytm_2)
      & k7_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),c4_8__arytm_1) = k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1) ) ),
    introduced(definition,[new_symbol(c4_8__arytm_1),file(arytm_1,c4_8__arytm_1)]),
    [interesting(0.8),axiom,file(arytm_1,c4_8__arytm_1)]).

fof(e3_8__arytm_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & k7_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),A) = k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[commutativity_k7_arytm_2,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1,t10_arytm_2]),
    [interesting(0.8),file(arytm_1,e3_8__arytm_1),[file(arytm_1,e3_8__arytm_1)]]).

fof(dt_c4_8__arytm_1,plain,(
    m1_subset_1(c4_8__arytm_1,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[dh_c4_8__arytm_1,e3_8__arytm_1]),
    [interesting(0.8),file(arytm_1,c4_8__arytm_1),[file(arytm_1,c4_8__arytm_1)]]).

fof(e4_8__arytm_1,plain,(
    k7_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),c4_8__arytm_1) = k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[dh_c4_8__arytm_1,e3_8__arytm_1]),
    [interesting(0.8),file(arytm_1,e4_8__arytm_1),[file(arytm_1,e4_8__arytm_1)]]).

fof(e5_8__arytm_1,plain,(
    k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1) = k7_arytm_2(k7_arytm_2(c1_8__arytm_1,c4_8__arytm_1),c3_8__arytm_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[commutativity_k7_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,dt_c4_8__arytm_1,e4_8__arytm_1,t7_arytm_2]),
    [interesting(0.8),file(arytm_1,e5_8__arytm_1),[file(arytm_1,e5_8__arytm_1)]]).

fof(t12_arytm_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( k7_arytm_2(A,B) = k7_arytm_2(A,C)
               => B = C ) ) ) ) ),
    file(arytm_2,t12_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t12_arytm_2)]).

fof(e6_8__arytm_1,plain,(
    c2_8__arytm_1 = k7_arytm_2(c1_8__arytm_1,c4_8__arytm_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[commutativity_k7_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,dt_c4_8__arytm_1,e5_8__arytm_1,t12_arytm_2]),
    [interesting(0.8),file(arytm_1,e6_8__arytm_1),[file(arytm_1,e6_8__arytm_1)]]).

fof(e7_8__arytm_1,plain,(
    r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[commutativity_k7_arytm_2,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_k7_arytm_2,dt_m1_subset_1,dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c4_8__arytm_1,e6_8__arytm_1,t20_arytm_2]),
    [interesting(0.8),file(arytm_1,e7_8__arytm_1),[file(arytm_1,e7_8__arytm_1)]]).

fof(i6_8__arytm_1,theorem,(
    $true ),
    introduced(tautology,[file(arytm_1,i6_8__arytm_1)]),
    [interesting(0.8),trivial,file(arytm_1,i6_8__arytm_1)]).

fof(i5_8__arytm_1,plain,(
    r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1,e2_8__arytm_1])],[e7_8__arytm_1,i6_8__arytm_1]),
    [interesting(0.8),file(arytm_1,i5_8__arytm_1),[file(arytm_1,i5_8__arytm_1)]]).

fof(i4_8__arytm_1,plain,
    ( r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1))
   => r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1]),discharge_asm(discharge,[e2_8__arytm_1])],[e2_8__arytm_1,i5_8__arytm_1]),
    [interesting(0.8),file(arytm_1,i4_8__arytm_1),[file(arytm_1,i4_8__arytm_1)]]).

fof(i3_8__arytm_1,plain,
    ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
  <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1,dt_c3_8__arytm_1])],[e1_8__arytm_1,i4_8__arytm_1]),
    [interesting(0.8),file(arytm_1,i3_8__arytm_1),[file(arytm_1,i3_8__arytm_1)]]).

fof(i3_8_tmp__arytm_1,plain,
    ( m1_subset_1(c3_8__arytm_1,k2_arytm_2)
   => ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
    <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,c3_8__arytm_1),k7_arytm_2(c2_8__arytm_1,c3_8__arytm_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1]),discharge_asm(discharge,[dt_c3_8__arytm_1])],[dt_c3_8__arytm_1,i3_8__arytm_1]),
    [interesting(0.8),i2_8__arytm_1]).

fof(i2_8__arytm_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
      <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,A),k7_arytm_2(c2_8__arytm_1,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__arytm_1,dt_c2_8__arytm_1])],[i3_8_tmp__arytm_1,dh_c3_8__arytm_1]),
    [interesting(0.8),file(arytm_1,i2_8__arytm_1),[file(arytm_1,i2_8__arytm_1)]]).

fof(i2_8_tmp__arytm_1,plain,
    ( m1_subset_1(c2_8__arytm_1,k2_arytm_2)
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ( r1_arytm_2(c1_8__arytm_1,c2_8__arytm_1)
        <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,A),k7_arytm_2(c2_8__arytm_1,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__arytm_1]),discharge_asm(discharge,[dt_c2_8__arytm_1])],[dt_c2_8__arytm_1,i2_8__arytm_1]),
    [interesting(0.8),i1_8__arytm_1]).

fof(i1_8__arytm_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( r1_arytm_2(c1_8__arytm_1,A)
          <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,B),k7_arytm_2(A,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__arytm_1])],[i2_8_tmp__arytm_1,dh_c2_8__arytm_1]),
    [interesting(0.8),file(arytm_1,i1_8__arytm_1),[file(arytm_1,i1_8__arytm_1)]]).

fof(i1_8_tmp__arytm_1,plain,
    ( m1_subset_1(c1_8__arytm_1,k2_arytm_2)
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ! [B] : 
            ( m1_subset_1(B,k2_arytm_2)
           => ( r1_arytm_2(c1_8__arytm_1,A)
            <=> r1_arytm_2(k7_arytm_2(c1_8__arytm_1,B),k7_arytm_2(A,B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__arytm_1])],[dt_c1_8__arytm_1,i1_8__arytm_1]),
    [interesting(1),t7_arytm_1]).

fof(t7_arytm_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( r1_arytm_2(A,B)
              <=> r1_arytm_2(k7_arytm_2(A,C),k7_arytm_2(B,C)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__arytm_1,dh_c1_8__arytm_1]),
    [interesting(1),file(arytm_1,t7_arytm_1),[file(arytm_1,t7_arytm_1)]]).