% Mizar ND problem: t7_arytm_0,arytm_0,111,36 
fof(dh_c1_8__arytm_0,definition,
    ( ! [A] : k13_arytm_3 != k4_tarski(c1_8__arytm_0,A)
   => ! [B,C] : k13_arytm_3 != k4_tarski(B,C) ),
    introduced(definition,[new_symbol(c1_8__arytm_0),file(arytm_0,c1_8__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_8__arytm_0)]).

fof(dh_c2_8__arytm_0,definition,
    ( k13_arytm_3 != k4_tarski(c1_8__arytm_0,c2_8__arytm_0)
   => ! [A] : k13_arytm_3 != k4_tarski(c1_8__arytm_0,A) ),
    introduced(definition,[new_symbol(c2_8__arytm_0),file(arytm_0,c2_8__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_8__arytm_0)]).

fof(e1_8__arytm_0,assumption,(
    k13_arytm_3 = k4_tarski(c1_8__arytm_0,c2_8__arytm_0) ),
    introduced(assumption,[file(arytm_0,e1_8__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,e1_8__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(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(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(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_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_c1_8__arytm_0,assumption,(
    $true ),
    introduced(assumption,[file(arytm_0,c1_8__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c1_8__arytm_0)]).

fof(dt_c2_8__arytm_0,assumption,(
    $true ),
    introduced(assumption,[file(arytm_0,c2_8__arytm_0)]),
    [interesting(0.8),axiom,file(arytm_0,c2_8__arytm_0)]).

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(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_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(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(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.9),axiom,file(tarski,d2_tarski)]).

fof(e3_8__arytm_0,plain,(
    r2_hidden(k1_tarski(c1_8__arytm_0),k2_tarski(k2_tarski(c1_8__arytm_0,c2_8__arytm_0),k1_tarski(c1_8__arytm_0))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_0,dt_c2_8__arytm_0])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_tarski,dt_c1_8__arytm_0,dt_c2_8__arytm_0,fc2_subset_1,fc3_subset_1,t1_subset,t7_boole,d2_tarski]),
    [interesting(0.8),file(arytm_0,e3_8__arytm_0),[file(arytm_0,e3_8__arytm_0)]]).

fof(cc1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(cc4_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ( v3_ordinal1(A)
       => ( v1_ordinal1(A)
          & v2_ordinal1(A)
          & v3_ordinal1(A)
          & v4_ordinal2(A) ) ) ) ),
    file(arytm_3,cc4_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc4_arytm_3)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(rc2_arytm_3,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(arytm_3,rc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc2_arytm_3)]).

fof(rc3_arytm_3,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc3_arytm_3)]).

fof(redefinition_k13_arytm_3,definition,(
    k13_arytm_3 = k4_ordinal2 ),
    file(arytm_3,k13_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k13_arytm_3)]).

fof(dt_k13_arytm_3,axiom,
    ( ~ v1_xboole_0(k13_arytm_3)
    & v3_ordinal1(k13_arytm_3)
    & m1_subset_1(k13_arytm_3,k6_arytm_3) ),
    file(arytm_3,k13_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k13_arytm_3)]).

fof(dt_k4_ordinal2,axiom,
    ( v3_ordinal1(k4_ordinal2)
    & ~ v1_xboole_0(k4_ordinal2) ),
    file(ordinal2,k4_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k4_ordinal2)]).

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

fof(fc1_arytm_3,theorem,
    ( ~ v1_xboole_0(k4_ordinal2)
    & v1_ordinal1(k4_ordinal2)
    & v2_ordinal1(k4_ordinal2)
    & v3_ordinal1(k4_ordinal2)
    & v4_ordinal2(k4_ordinal2) ),
    file(arytm_3,fc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc1_arytm_3)]).

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(t18_ordinal3,theorem,(
    k4_ordinal2 = k1_tarski(k1_xboole_0) ),
    file(ordinal3,t18_ordinal3),
    [interesting(0.9),axiom,file(ordinal3,t18_ordinal3)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(e2_8__arytm_0,plain,(
    k1_tarski(k12_arytm_3) = k2_tarski(k2_tarski(c1_8__arytm_0,c2_8__arytm_0),k1_tarski(c1_8__arytm_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_0,dt_c2_8__arytm_0,e1_8__arytm_0])],[antisymmetry_r2_hidden,t1_subset,existence_m1_subset_1,dt_k6_arytm_3,dt_m1_subset_1,cc1_arytm_3,cc2_arytm_3,cc4_arytm_3,fc8_arytm_3,rc1_arytm_3,rc1_xboole_0,rc2_arytm_3,rc2_xboole_0,rc3_arytm_3,t2_subset,t7_boole,t8_boole,commutativity_k2_tarski,redefinition_k12_arytm_3,redefinition_k13_arytm_3,dt_k12_arytm_3,dt_k13_arytm_3,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k4_ordinal2,dt_k4_tarski,dt_c1_8__arytm_0,dt_c2_8__arytm_0,fc1_arytm_3,fc1_xboole_0,fc1_zfmisc_1,fc2_subset_1,fc3_subset_1,t6_boole,e1_8__arytm_0,t18_ordinal3,d5_tarski]),
    [interesting(0.8),file(arytm_0,e2_8__arytm_0),[file(arytm_0,e2_8__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(e4_8__arytm_0,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__arytm_0,dt_c2_8__arytm_0,e1_8__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,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_tarski,dt_k2_tarski,dt_c1_8__arytm_0,dt_c2_8__arytm_0,fc2_subset_1,fc3_subset_1,t1_subset,t7_boole,e3_8__arytm_0,e2_8__arytm_0,d1_tarski]),
    [interesting(0.8),file(arytm_0,e4_8__arytm_0),[file(arytm_0,e4_8__arytm_0)]]).

fof(i3_8__arytm_0,theorem,(
    $true ),
    introduced(tautology,[file(arytm_0,i3_8__arytm_0)]),
    [interesting(0.8),trivial,file(arytm_0,i3_8__arytm_0)]).

fof(i2_8__arytm_0,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__arytm_0,dt_c2_8__arytm_0,e1_8__arytm_0])],[e4_8__arytm_0,i3_8__arytm_0]),
    [interesting(0.8),file(arytm_0,i2_8__arytm_0),[file(arytm_0,i2_8__arytm_0)]]).

fof(i1_8__arytm_0,plain,(
    k13_arytm_3 != k4_tarski(c1_8__arytm_0,c2_8__arytm_0) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__arytm_0,dt_c2_8__arytm_0]),discharge_asm(discharge,[e1_8__arytm_0])],[e1_8__arytm_0,i2_8__arytm_0]),
    [interesting(0.8),file(arytm_0,i1_8__arytm_0),[file(arytm_0,i1_8__arytm_0)]]).

fof(i1_8_tmp__arytm_0,plain,(
    k13_arytm_3 != k4_tarski(c1_8__arytm_0,c2_8__arytm_0) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__arytm_0,dt_c2_8__arytm_0])],[dt_c1_8__arytm_0,dt_c2_8__arytm_0,i1_8__arytm_0]),
    [interesting(1),t7_arytm_0]).

fof(t7_arytm_0,theorem,(
    ! [A,B] : k13_arytm_3 != k4_tarski(A,B) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__arytm_0,dh_c1_8__arytm_0,dh_c2_8__arytm_0]),
    [interesting(1),file(arytm_0,t7_arytm_0),[file(arytm_0,t7_arytm_0)]]).