% Mizar ND problem: t6_arytm_0,arytm_0,100,55 
fof(dh_c1_7__arytm_0,definition,
    ( ( m1_subset_1(c1_7__arytm_0,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ( k2_arytm_1(c1_7__arytm_0,A) = k12_arytm_3
           => c1_7__arytm_0 = A ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k2_arytm_2)
       => ! [C] : 
            ( m1_subset_1(C,k2_arytm_2)
           => ( k2_arytm_1(B,C) = k12_arytm_3
             => B = C ) ) ) ),
    introduced(definition,[new_symbol(c1_7__arytm_0),file(arytm_0,c1_7__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_7__arytm_0)]).

fof(dh_c2_7__arytm_0,definition,
    ( ( m1_subset_1(c2_7__arytm_0,k2_arytm_2)
     => ( k2_arytm_1(c1_7__arytm_0,c2_7__arytm_0) = k12_arytm_3
       => c1_7__arytm_0 = c2_7__arytm_0 ) )
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ( k2_arytm_1(c1_7__arytm_0,A) = k12_arytm_3
         => c1_7__arytm_0 = A ) ) ),
    introduced(definition,[new_symbol(c2_7__arytm_0),file(arytm_0,c2_7__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_7__arytm_0)]).

fof(e2_7__arytm_0,assumption,(
    k2_arytm_1(c1_7__arytm_0,c2_7__arytm_0) = k12_arytm_3 ),
    introduced(assumption,[file(arytm_0,e2_7__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,e2_7__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_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k6_arytm_3)]).

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

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_c1_7__arytm_0,assumption,(
    m1_subset_1(c1_7__arytm_0,k2_arytm_2) ),
    introduced(assumption,[file(arytm_0,c1_7__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_7__arytm_0)]).

fof(dt_c2_7__arytm_0,assumption,(
    m1_subset_1(c2_7__arytm_0,k2_arytm_2) ),
    introduced(assumption,[file(arytm_0,c2_7__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_7__arytm_0)]).

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(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(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(dt_k2_arytm_1,axiom,(
    $true ),
    file(arytm_1,k2_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,k2_arytm_1)]).

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(e1_7__arytm_0,plain,(
    k12_arytm_3 != k4_tarski(k12_arytm_3,k1_arytm_1(c2_7__arytm_0,c1_7__arytm_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__arytm_0,dt_c2_7__arytm_0])],[antisymmetry_r2_hidden,t1_subset,existence_m1_subset_1,dt_k1_xboole_0,dt_k2_arytm_2,dt_k6_arytm_3,dt_m1_subset_1,fc1_xboole_0,fc2_arytm_2,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_arytm_1,dt_k4_tarski,dt_c1_7__arytm_0,dt_c2_7__arytm_0,fc1_zfmisc_1]),
    [interesting(0.8),file(arytm_0,e1_7__arytm_0),[file(arytm_0,e1_7__arytm_0)]]).

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(e3_7__arytm_0,plain,(
    r1_arytm_2(c2_7__arytm_0,c1_7__arytm_0) ),
    inference(mizar_by,[status(thm),assumptions([e2_7__arytm_0,dt_c1_7__arytm_0,dt_c2_7__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,connectedness_r1_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_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_7__arytm_0,dt_c2_7__arytm_0,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t6_boole,e2_7__arytm_0,e1_7__arytm_0,d2_arytm_1]),
    [interesting(0.8),file(arytm_0,e3_7__arytm_0),[file(arytm_0,e3_7__arytm_0)]]).

fof(e4_7__arytm_0,plain,(
    k1_arytm_1(c1_7__arytm_0,c2_7__arytm_0) = k12_arytm_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__arytm_0,dt_c2_7__arytm_0,e2_7__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,connectedness_r1_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_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_7__arytm_0,dt_c2_7__arytm_0,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t6_boole,e3_7__arytm_0,e2_7__arytm_0,d2_arytm_1]),
    [interesting(0.8),file(arytm_0,e4_7__arytm_0),[file(arytm_0,e4_7__arytm_0)]]).

fof(t10_arytm_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r1_arytm_2(A,B)
              & k1_arytm_1(B,A) = k1_xboole_0 )
           => A = B ) ) ) ),
    file(arytm_1,t10_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,t10_arytm_1)]).

fof(e5_7__arytm_0,plain,(
    c1_7__arytm_0 = c2_7__arytm_0 ),
    inference(mizar_by,[status(thm),assumptions([e2_7__arytm_0,dt_c1_7__arytm_0,dt_c2_7__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,connectedness_r1_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_m1_subset_1,dt_c1_7__arytm_0,dt_c2_7__arytm_0,fc1_xboole_0,fc2_arytm_2,t6_boole,e4_7__arytm_0,e3_7__arytm_0,t10_arytm_1]),
    [interesting(0.8),file(arytm_0,e5_7__arytm_0),[file(arytm_0,e5_7__arytm_0)]]).

fof(i3_7__arytm_0,theorem,(
    $true ),
    introduced(tautology,[file(arytm_0,i3_7__arytm_0)]),
    [interesting(0.8),trivial,file(arytm_0,i3_7__arytm_0)]).

fof(i2_7__arytm_0,plain,(
    c1_7__arytm_0 = c2_7__arytm_0 ),
    inference(conclusion,[status(thm),assumptions([e2_7__arytm_0,dt_c1_7__arytm_0,dt_c2_7__arytm_0])],[e5_7__arytm_0,i3_7__arytm_0]),
    [interesting(0.8),file(arytm_0,i2_7__arytm_0),[file(arytm_0,i2_7__arytm_0)]]).

fof(i1_7__arytm_0,plain,
    ( k2_arytm_1(c1_7__arytm_0,c2_7__arytm_0) = k12_arytm_3
   => c1_7__arytm_0 = c2_7__arytm_0 ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__arytm_0,dt_c2_7__arytm_0]),discharge_asm(discharge,[e2_7__arytm_0])],[e2_7__arytm_0,i2_7__arytm_0]),
    [interesting(0.8),file(arytm_0,i1_7__arytm_0),[file(arytm_0,i1_7__arytm_0)]]).

fof(i1_7_tmp__arytm_0,plain,
    ( ( m1_subset_1(c1_7__arytm_0,k2_arytm_2)
      & m1_subset_1(c2_7__arytm_0,k2_arytm_2) )
   => ( k2_arytm_1(c1_7__arytm_0,c2_7__arytm_0) = k12_arytm_3
     => c1_7__arytm_0 = c2_7__arytm_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__arytm_0,dt_c2_7__arytm_0])],[dt_c1_7__arytm_0,dt_c2_7__arytm_0,i1_7__arytm_0]),
    [interesting(1),t6_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 ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__arytm_0,dh_c1_7__arytm_0,dh_c2_7__arytm_0]),
    [interesting(1),file(arytm_0,t6_arytm_0),[file(arytm_0,t6_arytm_0)]]).