% Mizar ND problem: t1_arytm_0,arytm_0,36,14 
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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_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(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_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(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_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]).

fof(fc3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc3_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_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(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_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(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(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

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(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(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

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(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_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(fc1_numbers,theorem,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    [interesting(0.9),axiom,file(numbers,fc1_numbers)]).

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(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(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(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(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(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

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(e2_2__arytm_0,plain,(
    ~ r2_hidden(k4_tarski(k12_arytm_3,k12_arytm_3),k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([])],[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,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,t3_arytm_2]),
    [interesting(0.8),file(arytm_0,e2_2__arytm_0),[file(arytm_0,e2_2__arytm_0)]]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t7_xboole_1)]).

fof(e1_2__arytm_0,plain,(
    r1_tarski(k2_arytm_2,k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2))) ),
    inference(mizar_by,[status(thm),assumptions([])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,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,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,fc8_arytm_3,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_boole,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,fc2_arytm_2,fc2_subset_1,t3_subset,t7_xboole_1]),
    [interesting(0.8),file(arytm_0,e1_2__arytm_0),[file(arytm_0,e1_2__arytm_0)]]).

fof(d1_numbers,definition,(
    k1_numbers = k4_xboole_0(k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)),k1_tarski(k4_tarski(0,0))) ),
    file(numbers,d1_numbers),
    [interesting(0.9),axiom,file(numbers,d1_numbers)]).

fof(t40_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => ( r2_hidden(C,A)
        | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) ) ) ),
    file(zfmisc_1,t40_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t40_zfmisc_1)]).

fof(e3_2__arytm_0,plain,(
    r1_tarski(k2_arytm_2,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([])],[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,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,fc8_arytm_3,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_boole,t2_subset,t3_boole,t4_boole,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,dt_k4_xboole_0,fc1_numbers,fc1_zfmisc_1,fc2_arytm_2,fc2_subset_1,t1_subset,t3_subset,t7_boole,spc0_boole,e2_2__arytm_0,e1_2__arytm_0,d1_numbers,t40_zfmisc_1]),
    [interesting(0.8),file(arytm_0,e3_2__arytm_0),[file(arytm_0,e3_2__arytm_0)]]).

fof(i1_2__arytm_0,theorem,(
    $true ),
    introduced(tautology,[file(arytm_0,i1_2__arytm_0)]),
    [interesting(0.8),trivial,file(arytm_0,i1_2__arytm_0)]).

fof(t1_arytm_0,theorem,(
    r1_tarski(k2_arytm_2,k1_numbers) ),
    inference(conclusion,[status(thm),assumptions([])],[e3_2__arytm_0,i1_2__arytm_0]),
    [interesting(1),file(arytm_0,t1_arytm_0),[file(arytm_0,t1_arytm_0)]]).