% Mizar ND problem: t8_arytm_0,arytm_0,121,12 
fof(dh_c1_9__arytm_0,definition,
    ( ( m1_subset_1(c1_9__arytm_0,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ! [B] : 
              ( m1_subset_1(B,k2_arytm_2)
             => ( k8_arytm_2(c1_9__arytm_0,A) = k8_arytm_2(c1_9__arytm_0,B)
               => ( c1_9__arytm_0 = k12_arytm_3
                  | 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)
               => ( k8_arytm_2(C,D) = k8_arytm_2(C,E)
                 => ( C = k12_arytm_3
                    | D = E ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_9__arytm_0),file(arytm_0,c1_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_9__arytm_0)]).

fof(dh_c2_9__arytm_0,definition,
    ( ( m1_subset_1(c2_9__arytm_0,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ( k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0) = k8_arytm_2(c1_9__arytm_0,A)
           => ( c1_9__arytm_0 = k12_arytm_3
              | c2_9__arytm_0 = A ) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k2_arytm_2)
       => ! [C] : 
            ( m1_subset_1(C,k2_arytm_2)
           => ( k8_arytm_2(c1_9__arytm_0,B) = k8_arytm_2(c1_9__arytm_0,C)
             => ( c1_9__arytm_0 = k12_arytm_3
                | B = C ) ) ) ) ),
    introduced(definition,[new_symbol(c2_9__arytm_0),file(arytm_0,c2_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_9__arytm_0)]).

fof(dh_c3_9__arytm_0,definition,
    ( ( m1_subset_1(c3_9__arytm_0,k2_arytm_2)
     => ( k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0) = k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0)
       => ( c1_9__arytm_0 = k12_arytm_3
          | c2_9__arytm_0 = c3_9__arytm_0 ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ( k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0) = k8_arytm_2(c1_9__arytm_0,A)
         => ( c1_9__arytm_0 = k12_arytm_3
            | c2_9__arytm_0 = A ) ) ) ),
    introduced(definition,[new_symbol(c3_9__arytm_0),file(arytm_0,c3_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c3_9__arytm_0)]).

fof(e1_9__arytm_0,assumption,(
    c1_9__arytm_0 != k12_arytm_3 ),
    introduced(assumption,[file(arytm_0,e1_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,e1_9__arytm_0)]).

fof(e2_9__arytm_0,assumption,(
    k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0) = k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0) ),
    introduced(assumption,[file(arytm_0,e2_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,e2_9__arytm_0)]).

fof(e1_9_1_1__arytm_0,assumption,(
    r1_arytm_2(c3_9__arytm_0,c2_9__arytm_0) ),
    introduced(assumption,[file(arytm_0,e1_9_1_1__arytm_0)]),
    [interesting(0.5),axiom,file(arytm_0,e1_9_1_1__arytm_0)]).

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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k6_arytm_3)]).

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(fc8_arytm_3,theorem,(
    ~ v1_xboole_0(k6_arytm_3) ),
    file(arytm_3,fc8_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc8_arytm_3)]).

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(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(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(redefinition_k12_arytm_3,definition,(
    k12_arytm_3 = k1_xboole_0 ),
    file(arytm_3,k12_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k12_arytm_3)]).

fof(dt_k12_arytm_3,axiom,
    ( v1_xboole_0(k12_arytm_3)
    & m1_subset_1(k12_arytm_3,k6_arytm_3) ),
    file(arytm_3,k12_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k12_arytm_3)]).

fof(dt_k2_arytm_1,axiom,(
    $true ),
    file(arytm_1,k2_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,k2_arytm_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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_c2_9__arytm_0,assumption,(
    m1_subset_1(c2_9__arytm_0,k2_arytm_2) ),
    introduced(assumption,[file(arytm_0,c2_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_9__arytm_0)]).

fof(dt_c3_9__arytm_0,assumption,(
    m1_subset_1(c3_9__arytm_0,k2_arytm_2) ),
    introduced(assumption,[file(arytm_0,c3_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c3_9__arytm_0)]).

fof(fc2_arytm_2,theorem,(
    ~ v1_xboole_0(k2_arytm_2) ),
    file(arytm_2,fc2_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,fc2_arytm_2)]).

fof(commutativity_k8_arytm_2,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => k8_arytm_2(A,B) = k8_arytm_2(B,A) ) ),
    file(arytm_2,k8_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,k8_arytm_2)]).

fof(dt_k1_arytm_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => m1_subset_1(k1_arytm_1(A,B),k2_arytm_2) ) ),
    file(arytm_1,k1_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,k1_arytm_1)]).

fof(dt_k8_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => m1_subset_1(k8_arytm_2(A,B),k2_arytm_2) ) ),
    file(arytm_2,k8_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,k8_arytm_2)]).

fof(dt_c1_9__arytm_0,assumption,(
    m1_subset_1(c1_9__arytm_0,k2_arytm_2) ),
    introduced(assumption,[file(arytm_0,c1_9__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_9__arytm_0)]).

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(t26_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)
               => k8_arytm_2(C,k1_arytm_1(B,A)) = k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) ) ) ) ) ),
    file(arytm_1,t26_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,t26_arytm_1)]).

fof(e1_9_1_1_1__arytm_0,plain,(
    k8_arytm_2(c1_9__arytm_0,k1_arytm_1(c2_9__arytm_0,c3_9__arytm_0)) = k2_arytm_1(k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0),k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_1__arytm_0])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k8_arytm_2,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k1_arytm_1,dt_k2_arytm_1,dt_k2_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc2_arytm_2,e1_9_1_1__arytm_0,t26_arytm_1]),
    [interesting(0.35),file(arytm_0,e1_9_1_1_1__arytm_0),[file(arytm_0,e1_9_1_1_1__arytm_0)]]).

fof(t18_arytm_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => k2_arytm_1(A,A) = k1_xboole_0 ) ),
    file(arytm_1,t18_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,t18_arytm_1)]).

fof(e2_9_1_1_1__arytm_0,plain,(
    k2_arytm_1(k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0),k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0)) = k12_arytm_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e2_9__arytm_0])],[antisymmetry_r2_hidden,t1_subset,dt_k6_arytm_3,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,commutativity_k8_arytm_2,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_xboole_0,dt_k2_arytm_1,dt_k2_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc1_xboole_0,fc2_arytm_2,t6_boole,e2_9__arytm_0,t18_arytm_1]),
    [interesting(0.35),file(arytm_0,e2_9_1_1_1__arytm_0),[file(arytm_0,e2_9_1_1_1__arytm_0)]]).

fof(e2_9_1_1__arytm_0,plain,(
    k8_arytm_2(c1_9__arytm_0,k1_arytm_1(c2_9__arytm_0,c3_9__arytm_0)) = k12_arytm_3 ),
    inference(iterative_eq,[status(thm),assumptions([e1_9_1_1__arytm_0,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e2_9__arytm_0])],[e1_9_1_1_1__arytm_0,e2_9_1_1_1__arytm_0]),
    [interesting(0.5),file(arytm_0,e2_9_1_1__arytm_0),[file(arytm_0,e2_9_1_1__arytm_0)]]).

fof(t2_arytm_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ~ ( k8_arytm_2(A,B) = k1_xboole_0
              & A != k1_xboole_0
              & B != k1_xboole_0 ) ) ) ),
    file(arytm_1,t2_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,t2_arytm_1)]).

fof(e1_9_1_1_2__arytm_0,plain,(
    k12_arytm_3 = k1_arytm_1(c2_9__arytm_0,c3_9__arytm_0) ),
    inference(mizar_by,[status(thm),assumptions([e1_9_1_1__arytm_0,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0])],[antisymmetry_r2_hidden,t1_subset,dt_k6_arytm_3,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,commutativity_k8_arytm_2,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_arytm_1,dt_k1_xboole_0,dt_k2_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc1_xboole_0,fc2_arytm_2,t6_boole,e2_9_1_1__arytm_0,e1_9__arytm_0,t2_arytm_1]),
    [interesting(0.35),file(arytm_0,e1_9_1_1_2__arytm_0),[file(arytm_0,e1_9_1_1_2__arytm_0)]]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(fc1_zfmisc_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,fc1_zfmisc_1)]).

fof(d2_arytm_1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r1_arytm_2(B,A)
             => k2_arytm_1(A,B) = k1_arytm_1(A,B) )
            & ( ~ r1_arytm_2(B,A)
             => k2_arytm_1(A,B) = k4_tarski(k1_xboole_0,k1_arytm_1(B,A)) ) ) ) ) ),
    file(arytm_1,d2_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,d2_arytm_1)]).

fof(e2_9_1_1_2__arytm_0,plain,(
    k1_arytm_1(c2_9__arytm_0,c3_9__arytm_0) = k2_arytm_1(c2_9__arytm_0,c3_9__arytm_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_1__arytm_0])],[antisymmetry_r2_hidden,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k1_arytm_1,dt_k1_xboole_0,dt_k2_arytm_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t6_boole,e1_9_1_1__arytm_0,d2_arytm_1]),
    [interesting(0.35),file(arytm_0,e2_9_1_1_2__arytm_0),[file(arytm_0,e2_9_1_1_2__arytm_0)]]).

fof(e3_9_1_1__arytm_0,plain,(
    k12_arytm_3 = k2_arytm_1(c2_9__arytm_0,c3_9__arytm_0) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_1__arytm_0])],[e1_9_1_1_2__arytm_0,e2_9_1_1_2__arytm_0]),
    [interesting(0.5),file(arytm_0,e3_9_1_1__arytm_0),[file(arytm_0,e3_9_1_1__arytm_0)]]).

fof(t6_arytm_0,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( k2_arytm_1(A,B) = k12_arytm_3
           => A = B ) ) ) ),
    file(arytm_0,t6_arytm_0),
    [interesting(0.9),axiom,file(arytm_0,t6_arytm_0)]).

fof(e4_9_1_1__arytm_0,plain,(
    c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_1__arytm_0])],[antisymmetry_r2_hidden,t1_subset,dt_k1_xboole_0,dt_k6_arytm_3,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k2_arytm_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc2_arytm_2,e3_9_1_1__arytm_0,t6_arytm_0]),
    [interesting(0.5),file(arytm_0,e4_9_1_1__arytm_0),[file(arytm_0,e4_9_1_1__arytm_0)]]).

fof(i2_9_1_1__arytm_0,theorem,(
    $true ),
    introduced(tautology,[file(arytm_0,i2_9_1_1__arytm_0)]),
    [interesting(0.5),trivial,file(arytm_0,i2_9_1_1__arytm_0)]).

fof(i1_9_1_1__arytm_0,plain,(
    c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_1__arytm_0])],[e4_9_1_1__arytm_0,i2_9_1_1__arytm_0]),
    [interesting(0.5),file(arytm_0,i1_9_1_1__arytm_0),[file(arytm_0,i1_9_1_1__arytm_0)]]).

fof(i1_9_1__arytm_0,plain,
    ( r1_arytm_2(c3_9__arytm_0,c2_9__arytm_0)
   => c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0]),discharge_asm(discharge,[e1_9_1_1__arytm_0])],[e1_9_1_1__arytm_0,i1_9_1_1__arytm_0]),
    [interesting(0.65),file(arytm_0,i1_9_1__arytm_0),[file(arytm_0,i1_9_1__arytm_0)]]).

fof(e1_9_1_2__arytm_0,assumption,(
    r1_arytm_2(c2_9__arytm_0,c3_9__arytm_0) ),
    introduced(assumption,[file(arytm_0,e1_9_1_2__arytm_0)]),
    [interesting(0.5),axiom,file(arytm_0,e1_9_1_2__arytm_0)]).

fof(e1_9_1_2_1__arytm_0,plain,(
    k8_arytm_2(c1_9__arytm_0,k1_arytm_1(c3_9__arytm_0,c2_9__arytm_0)) = k2_arytm_1(k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0),k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_2__arytm_0])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k8_arytm_2,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k1_arytm_1,dt_k2_arytm_1,dt_k2_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc2_arytm_2,e1_9_1_2__arytm_0,t26_arytm_1]),
    [interesting(0.35),file(arytm_0,e1_9_1_2_1__arytm_0),[file(arytm_0,e1_9_1_2_1__arytm_0)]]).

fof(e2_9_1_2_1__arytm_0,plain,(
    k2_arytm_1(k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0),k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0)) = k12_arytm_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e2_9__arytm_0])],[antisymmetry_r2_hidden,t1_subset,dt_k6_arytm_3,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,commutativity_k8_arytm_2,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_xboole_0,dt_k2_arytm_1,dt_k2_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc1_xboole_0,fc2_arytm_2,t6_boole,e2_9__arytm_0,t18_arytm_1]),
    [interesting(0.35),file(arytm_0,e2_9_1_2_1__arytm_0),[file(arytm_0,e2_9_1_2_1__arytm_0)]]).

fof(e2_9_1_2__arytm_0,plain,(
    k8_arytm_2(c1_9__arytm_0,k1_arytm_1(c3_9__arytm_0,c2_9__arytm_0)) = k12_arytm_3 ),
    inference(iterative_eq,[status(thm),assumptions([e1_9_1_2__arytm_0,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e2_9__arytm_0])],[e1_9_1_2_1__arytm_0,e2_9_1_2_1__arytm_0]),
    [interesting(0.5),file(arytm_0,e2_9_1_2__arytm_0),[file(arytm_0,e2_9_1_2__arytm_0)]]).

fof(e1_9_1_2_2__arytm_0,plain,(
    k12_arytm_3 = k1_arytm_1(c3_9__arytm_0,c2_9__arytm_0) ),
    inference(mizar_by,[status(thm),assumptions([e1_9_1_2__arytm_0,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0])],[antisymmetry_r2_hidden,t1_subset,dt_k6_arytm_3,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,commutativity_k8_arytm_2,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_arytm_1,dt_k1_xboole_0,dt_k2_arytm_2,dt_k8_arytm_2,dt_m1_subset_1,dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc1_xboole_0,fc2_arytm_2,t6_boole,e2_9_1_2__arytm_0,e1_9__arytm_0,t2_arytm_1]),
    [interesting(0.35),file(arytm_0,e1_9_1_2_2__arytm_0),[file(arytm_0,e1_9_1_2_2__arytm_0)]]).

fof(e2_9_1_2_2__arytm_0,plain,(
    k1_arytm_1(c3_9__arytm_0,c2_9__arytm_0) = k2_arytm_1(c3_9__arytm_0,c2_9__arytm_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_2__arytm_0])],[antisymmetry_r2_hidden,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k1_arytm_1,dt_k1_xboole_0,dt_k2_arytm_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t6_boole,e1_9_1_2__arytm_0,d2_arytm_1]),
    [interesting(0.35),file(arytm_0,e2_9_1_2_2__arytm_0),[file(arytm_0,e2_9_1_2_2__arytm_0)]]).

fof(e3_9_1_2__arytm_0,plain,(
    k12_arytm_3 = k2_arytm_1(c3_9__arytm_0,c2_9__arytm_0) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_2__arytm_0])],[e1_9_1_2_2__arytm_0,e2_9_1_2_2__arytm_0]),
    [interesting(0.5),file(arytm_0,e3_9_1_2__arytm_0),[file(arytm_0,e3_9_1_2__arytm_0)]]).

fof(e4_9_1_2__arytm_0,plain,(
    c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_2__arytm_0])],[antisymmetry_r2_hidden,t1_subset,dt_k1_xboole_0,dt_k6_arytm_3,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k2_arytm_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_9__arytm_0,dt_c3_9__arytm_0,fc2_arytm_2,e3_9_1_2__arytm_0,t6_arytm_0]),
    [interesting(0.5),file(arytm_0,e4_9_1_2__arytm_0),[file(arytm_0,e4_9_1_2__arytm_0)]]).

fof(i2_9_1_2__arytm_0,theorem,(
    $true ),
    introduced(tautology,[file(arytm_0,i2_9_1_2__arytm_0)]),
    [interesting(0.5),trivial,file(arytm_0,i2_9_1_2__arytm_0)]).

fof(i1_9_1_2__arytm_0,plain,(
    c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,e1_9_1_2__arytm_0])],[e4_9_1_2__arytm_0,i2_9_1_2__arytm_0]),
    [interesting(0.5),file(arytm_0,i1_9_1_2__arytm_0),[file(arytm_0,i1_9_1_2__arytm_0)]]).

fof(i2_9_1__arytm_0,plain,
    ( r1_arytm_2(c2_9__arytm_0,c3_9__arytm_0)
   => c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0]),discharge_asm(discharge,[e1_9_1_2__arytm_0])],[e1_9_1_2__arytm_0,i1_9_1_2__arytm_0]),
    [interesting(0.65),file(arytm_0,i2_9_1__arytm_0),[file(arytm_0,i2_9_1__arytm_0)]]).

fof(e1_9_1__arytm_0,plain,
    ( r1_arytm_2(c3_9__arytm_0,c2_9__arytm_0)
    | r1_arytm_2(c2_9__arytm_0,c3_9__arytm_0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_9__arytm_0,dt_c3_9__arytm_0])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,fc2_arytm_2,connectedness_r1_arytm_2,dt_c2_9__arytm_0,dt_c3_9__arytm_0]),
    [interesting(0.65),file(arytm_0,e1_9_1__arytm_0),[file(arytm_0,e1_9_1__arytm_0)]]).

fof(i2_9__arytm_0,plain,(
    c2_9__arytm_0 = c3_9__arytm_0 ),
    inference(percases,[status(thm),assumptions([dt_c1_9__arytm_0,e2_9__arytm_0,e1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0])],[i1_9_1__arytm_0,i2_9_1__arytm_0,e1_9_1__arytm_0]),
    [interesting(0.8),file(arytm_0,i2_9__arytm_0),[file(arytm_0,i2_9__arytm_0)]]).

fof(i1_9__arytm_0,plain,
    ( k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0) = k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0)
   => ( c1_9__arytm_0 = k12_arytm_3
      | c2_9__arytm_0 = c3_9__arytm_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0]),discharge_asm(discharge,[e1_9__arytm_0,e2_9__arytm_0])],[e1_9__arytm_0,e2_9__arytm_0,i2_9__arytm_0]),
    [interesting(0.8),file(arytm_0,i1_9__arytm_0),[file(arytm_0,i1_9__arytm_0)]]).

fof(i1_9_tmp__arytm_0,plain,
    ( ( m1_subset_1(c1_9__arytm_0,k2_arytm_2)
      & m1_subset_1(c2_9__arytm_0,k2_arytm_2)
      & m1_subset_1(c3_9__arytm_0,k2_arytm_2) )
   => ( k8_arytm_2(c1_9__arytm_0,c2_9__arytm_0) = k8_arytm_2(c1_9__arytm_0,c3_9__arytm_0)
     => ( c1_9__arytm_0 = k12_arytm_3
        | c2_9__arytm_0 = c3_9__arytm_0 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0])],[dt_c1_9__arytm_0,dt_c2_9__arytm_0,dt_c3_9__arytm_0,i1_9__arytm_0]),
    [interesting(1),t8_arytm_0]).

fof(t8_arytm_0,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)
             => ( k8_arytm_2(A,B) = k8_arytm_2(A,C)
               => ( A = k12_arytm_3
                  | B = C ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_9_tmp__arytm_0,dh_c1_9__arytm_0,dh_c2_9__arytm_0,dh_c3_9__arytm_0]),
    [interesting(1),file(arytm_0,t8_arytm_0),[file(arytm_0,t8_arytm_0)]]).