% Mizar ND problem: t5_arytm_0,arytm_0,84,26 
fof(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

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(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_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(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

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(symmetry_r1_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r1_subset_1(A,B)
       => r1_subset_1(B,A) ) ) ),
    file(subset_1,r1_subset_1),
    [interesting(0.9),axiom,file(subset_1,r1_subset_1)]).

fof(irreflexivity_r1_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r1_subset_1(A,A) ) ),
    file(subset_1,r1_subset_1),
    [interesting(0.9),axiom,file(subset_1,r1_subset_1)]).

fof(symmetry_r2_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_subset_1(A,B)
       => r2_subset_1(B,A) ) ) ),
    file(subset_1,r2_subset_1),
    [interesting(0.9),axiom,file(subset_1,r2_subset_1)]).

fof(irreflexivity_r2_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r2_subset_1(A,A) ) ),
    file(subset_1,r2_subset_1),
    [interesting(0.9),axiom,file(subset_1,r2_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(redefinition_r1_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r1_subset_1(A,B)
      <=> r1_xboole_0(A,B) ) ) ),
    file(subset_1,r1_subset_1),
    [interesting(0.9),axiom,file(subset_1,r1_subset_1)]).

fof(redefinition_r2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r2_subset_1(A,B)
      <=> r1_xboole_0(A,B) ) ) ),
    file(subset_1,r2_subset_1),
    [interesting(0.9),axiom,file(subset_1,r2_subset_1)]).

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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

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(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(e1_6__arytm_0,assumption,(
    ~ r2_subset_1(k2_arytm_2,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ),
    introduced(assumption,[file(arytm_0,e1_6__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,e1_6__arytm_0)]).

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

fof(dh_c1_6__arytm_0,definition,
    ( ? [A] : 
        ( r2_hidden(A,k2_arytm_2)
        & r2_hidden(A,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) )
   => ( r2_hidden(c1_6__arytm_0,k2_arytm_2)
      & r2_hidden(c1_6__arytm_0,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ) ),
    introduced(definition,[new_symbol(c1_6__arytm_0),file(arytm_0,c1_6__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_6__arytm_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(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(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : 
              ~ ( r2_hidden(C,A)
                & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,t3_xboole_0)]).

fof(e2_6__arytm_0,plain,(
    ? [A] : 
      ( r2_hidden(A,k2_arytm_2)
      & r2_hidden(A,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_6__arytm_0])],[existence_m1_subset_1,dt_k1_xboole_0,dt_k6_arytm_3,dt_m1_subset_1,fc1_xboole_0,fc4_subset_1,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,symmetry_r2_subset_1,irreflexivity_r2_subset_1,redefinition_k12_arytm_3,redefinition_r2_subset_1,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,fc2_arytm_2,fc2_subset_1,t1_subset,t7_boole,e1_6__arytm_0,t3_xboole_0]),
    [interesting(0.8),file(arytm_0,e2_6__arytm_0),[file(arytm_0,e2_6__arytm_0)]]).

fof(dt_c1_6__arytm_0,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c1_6__arytm_0,e2_6__arytm_0]),
    [interesting(0.8),file(arytm_0,c1_6__arytm_0),[file(arytm_0,c1_6__arytm_0)]]).

fof(dh_c2_6__arytm_0,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,k1_tarski(k12_arytm_3))
        & r2_hidden(B,k2_arytm_2)
        & c1_6__arytm_0 = k4_tarski(A,B) )
   => ? [C] : 
        ( r2_hidden(c2_6__arytm_0,k1_tarski(k12_arytm_3))
        & r2_hidden(C,k2_arytm_2)
        & c1_6__arytm_0 = k4_tarski(c2_6__arytm_0,C) ) ),
    introduced(definition,[new_symbol(c2_6__arytm_0),file(arytm_0,c2_6__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_6__arytm_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(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_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(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(e4_6__arytm_0,plain,(
    r2_hidden(c1_6__arytm_0,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c1_6__arytm_0,e2_6__arytm_0]),
    [interesting(0.8),file(arytm_0,e4_6__arytm_0),[file(arytm_0,e4_6__arytm_0)]]).

fof(t103_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r2_hidden(D,A)
        & ! [E,F] : 
            ~ ( r2_hidden(E,B)
              & r2_hidden(F,C)
              & D = k4_tarski(E,F) ) ) ),
    file(zfmisc_1,t103_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t103_zfmisc_1)]).

fof(e5_6__arytm_0,plain,(
    ? [A,B] : 
      ( r2_hidden(A,k1_tarski(k12_arytm_3))
      & r2_hidden(B,k2_arytm_2)
      & c1_6__arytm_0 = k4_tarski(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_6__arytm_0])],[existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k6_arytm_3,dt_m1_subset_1,fc1_subset_1,fc1_xboole_0,fc4_subset_1,fc8_arytm_3,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__arytm_0,fc1_zfmisc_1,fc2_arytm_2,fc2_subset_1,t1_subset,t3_subset,t7_boole,e4_6__arytm_0,t103_zfmisc_1]),
    [interesting(0.8),file(arytm_0,e5_6__arytm_0),[file(arytm_0,e5_6__arytm_0)]]).

fof(dt_c2_6__arytm_0,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c2_6__arytm_0,e5_6__arytm_0]),
    [interesting(0.8),file(arytm_0,c2_6__arytm_0),[file(arytm_0,c2_6__arytm_0)]]).

fof(dh_c3_6__arytm_0,definition,
    ( ? [A] : 
        ( r2_hidden(c2_6__arytm_0,k1_tarski(k12_arytm_3))
        & r2_hidden(A,k2_arytm_2)
        & c1_6__arytm_0 = k4_tarski(c2_6__arytm_0,A) )
   => ( r2_hidden(c2_6__arytm_0,k1_tarski(k12_arytm_3))
      & r2_hidden(c3_6__arytm_0,k2_arytm_2)
      & c1_6__arytm_0 = k4_tarski(c2_6__arytm_0,c3_6__arytm_0) ) ),
    introduced(definition,[new_symbol(c3_6__arytm_0),file(arytm_0,c3_6__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c3_6__arytm_0)]).

fof(dt_c3_6__arytm_0,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c2_6__arytm_0,dh_c3_6__arytm_0,e5_6__arytm_0]),
    [interesting(0.8),file(arytm_0,c3_6__arytm_0),[file(arytm_0,c3_6__arytm_0)]]).

fof(e6_6__arytm_0,plain,(
    r2_hidden(c2_6__arytm_0,k1_tarski(k12_arytm_3)) ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c2_6__arytm_0,dh_c3_6__arytm_0,e5_6__arytm_0]),
    [interesting(0.8),file(arytm_0,e6_6__arytm_0),[file(arytm_0,e6_6__arytm_0)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e8_6__arytm_0,plain,(
    c2_6__arytm_0 = k12_arytm_3 ),
    inference(mizar_by,[status(thm),assumptions([e1_6__arytm_0])],[existence_m1_subset_1,dt_k1_xboole_0,dt_k6_arytm_3,dt_m1_subset_1,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_tarski,dt_c2_6__arytm_0,fc2_subset_1,t1_subset,t7_boole,e6_6__arytm_0,d1_tarski]),
    [interesting(0.8),file(arytm_0,e8_6__arytm_0),[file(arytm_0,e8_6__arytm_0)]]).

fof(e3_6__arytm_0,plain,(
    r2_hidden(c1_6__arytm_0,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c1_6__arytm_0,e2_6__arytm_0]),
    [interesting(0.8),file(arytm_0,e3_6__arytm_0),[file(arytm_0,e3_6__arytm_0)]]).

fof(e7_6__arytm_0,plain,
    ( r2_hidden(c3_6__arytm_0,k2_arytm_2)
    & c1_6__arytm_0 = k4_tarski(c2_6__arytm_0,c3_6__arytm_0) ),
    inference(consider,[status(thm),assumptions([e1_6__arytm_0])],[dh_c2_6__arytm_0,dh_c3_6__arytm_0,e5_6__arytm_0]),
    [interesting(0.8),file(arytm_0,e7_6__arytm_0),[file(arytm_0,e7_6__arytm_0)]]).

fof(t3_arytm_2,theorem,(
    ! [A] : ~ r2_hidden(k4_tarski(k12_arytm_3,A),k2_arytm_2) ),
    file(arytm_2,t3_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t3_arytm_2)]).

fof(e9_6__arytm_0,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_6__arytm_0])],[existence_m1_subset_1,dt_k1_xboole_0,dt_k6_arytm_3,dt_m1_subset_1,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k2_arytm_2,dt_k4_tarski,dt_c1_6__arytm_0,dt_c2_6__arytm_0,dt_c3_6__arytm_0,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,e8_6__arytm_0,e3_6__arytm_0,e7_6__arytm_0,t3_arytm_2]),
    [interesting(0.8),file(arytm_0,e9_6__arytm_0),[file(arytm_0,e9_6__arytm_0)]]).

fof(i2_6__arytm_0,theorem,(
    $true ),
    introduced(tautology,[file(arytm_0,i2_6__arytm_0)]),
    [interesting(0.8),trivial,file(arytm_0,i2_6__arytm_0)]).

fof(i1_6__arytm_0,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_6__arytm_0])],[e9_6__arytm_0,i2_6__arytm_0]),
    [interesting(0.8),file(arytm_0,i1_6__arytm_0),[file(arytm_0,i1_6__arytm_0)]]).

fof(i1_6_tmp__arytm_0,plain,
    ( ~ r2_subset_1(k2_arytm_2,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2))
   => ~ $true ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[e1_6__arytm_0])],[e1_6__arytm_0,i1_6__arytm_0]),
    [interesting(1),t5_arytm_0]).

fof(t5_arytm_0,theorem,(
    r1_subset_1(k2_arytm_2,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ),
    inference(mizar_def_expansion,[status(thm),assumptions([])],[i1_6_tmp__arytm_0,symmetry_r1_xboole_0,dt_k1_xboole_0,dt_k6_arytm_3,dt_m1_subset_1,fc1_xboole_0,fc4_subset_1,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,symmetry_r1_subset_1,irreflexivity_r1_subset_1,symmetry_r2_subset_1,irreflexivity_r2_subset_1,redefinition_k12_arytm_3,redefinition_r1_subset_1,redefinition_r2_subset_1,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,fc2_arytm_2,fc2_subset_1]),
    [interesting(1),file(arytm_0,t5_arytm_0),[file(arytm_0,t5_arytm_0)]]).