% Mizar ND problem: t3_arytm_3,arytm_3,148,47 
fof(dh_c1_10__arytm_3,definition,
    ( ( ( v3_ordinal1(c1_10__arytm_3)
        & v4_ordinal2(c1_10__arytm_3) )
     => ! [A] : 
          ( ( v3_ordinal1(A)
            & v4_ordinal2(A) )
         => k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3) ) )
   => ! [B] : 
        ( ( v3_ordinal1(B)
          & v4_ordinal2(B) )
       => ! [C] : 
            ( ( v3_ordinal1(C)
              & v4_ordinal2(C) )
           => k14_ordinal2(B,C) = k14_ordinal2(C,B) ) ) ),
    introduced(definition,[new_symbol(c1_10__arytm_3),file(arytm_3,c1_10__arytm_3)]),
    [interesting(0.8),axiom,file(arytm_3,c1_10__arytm_3)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

fof(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

fof(dt_k14_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => v3_ordinal1(k14_ordinal2(A,B)) ) ),
    file(ordinal2,k14_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k14_ordinal2)]).

fof(dt_c1_10__arytm_3,assumption,
    ( v3_ordinal1(c1_10__arytm_3)
    & v4_ordinal2(c1_10__arytm_3) ),
    introduced(assumption,[file(arytm_3,c1_10__arytm_3)]),
    [interesting(0.8),axiom,file(arytm_3,c1_10__arytm_3)]).

fof(cc1_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(fc3_arytm_3,theorem,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => ( v1_ordinal1(k14_ordinal2(A,B))
        & v2_ordinal1(k14_ordinal2(A,B))
        & v3_ordinal1(k14_ordinal2(A,B))
        & v4_ordinal2(k14_ordinal2(A,B)) ) ) ),
    file(arytm_3,fc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc3_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(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

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(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_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

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(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

fof(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,k1_ordinal1)]).

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

fof(fc1_ordinal1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc1_ordinal1)]).

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_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A))
        & v4_ordinal2(k1_ordinal1(A)) ) ) ),
    file(arytm_3,fc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc2_arytm_3)]).

fof(fc2_ordinal1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(fc3_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc3_ordinal1)]).

fof(s1_arytm_3__e4_10__arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ( k14_ordinal2(A,k1_xboole_0) = k14_ordinal2(k1_xboole_0,A)
          & ! [B] : 
              ( ( v3_ordinal1(B)
                & v4_ordinal2(B) )
             => ( k14_ordinal2(A,B) = k14_ordinal2(B,A)
               => k14_ordinal2(A,k1_ordinal1(B)) = k14_ordinal2(k1_ordinal1(B),A) ) ) )
       => ! [B] : 
            ( ( v3_ordinal1(B)
              & v4_ordinal2(B) )
           => k14_ordinal2(A,B) = k14_ordinal2(B,A) ) ) ) ),
    file(arytm_3,s1_arytm_3__e4_10__arytm_3),
    [interesting(0.9),axiom,file(arytm_3,s1_arytm_3__e4_10__arytm_3)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(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(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(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(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(t44_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k14_ordinal2(A,k1_xboole_0) = A ) ),
    file(ordinal2,t44_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,t44_ordinal2)]).

fof(e1_10_1__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_xboole_0) = c1_10__arytm_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,t2_subset,antisymmetry_r2_hidden,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_xboole_0,dt_c1_10__arytm_3,cc1_ordinal1,fc1_xboole_0,fc2_ordinal1,t6_boole,t44_ordinal2]),
    [interesting(0.65),file(arytm_3,e1_10_1__arytm_3),[file(arytm_3,e1_10_1__arytm_3)]]).

fof(t47_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k14_ordinal2(k1_xboole_0,A) = A ) ),
    file(ordinal2,t47_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,t47_ordinal2)]).

fof(e2_10_1__arytm_3,plain,(
    c1_10__arytm_3 = k14_ordinal2(k1_xboole_0,c1_10__arytm_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,t2_subset,antisymmetry_r2_hidden,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_xboole_0,dt_c1_10__arytm_3,cc1_ordinal1,fc1_xboole_0,fc2_ordinal1,t6_boole,t47_ordinal2]),
    [interesting(0.65),file(arytm_3,e2_10_1__arytm_3),[file(arytm_3,e2_10_1__arytm_3)]]).

fof(e1_10__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_xboole_0) = k14_ordinal2(k1_xboole_0,c1_10__arytm_3) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_10__arytm_3])],[e1_10_1__arytm_3,e2_10_1__arytm_3]),
    [interesting(0.8),file(arytm_3,e1_10__arytm_3),[file(arytm_3,e1_10__arytm_3)]]).

fof(e2_10__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_xboole_0) = k14_ordinal2(k1_xboole_0,c1_10__arytm_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_xboole_0,dt_c1_10__arytm_3,fc1_xboole_0,fc2_ordinal1,t6_boole,e1_10__arytm_3]),
    [interesting(0.8),file(arytm_3,e2_10__arytm_3),[file(arytm_3,e2_10__arytm_3)]]).

fof(dh_c1_10_2__arytm_3,definition,
    ( ( ( v3_ordinal1(c1_10_2__arytm_3)
        & v4_ordinal2(c1_10_2__arytm_3) )
     => ( k14_ordinal2(c1_10__arytm_3,c1_10_2__arytm_3) = k14_ordinal2(c1_10_2__arytm_3,c1_10__arytm_3)
       => k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ) )
   => ! [A] : 
        ( ( v3_ordinal1(A)
          & v4_ordinal2(A) )
       => ( k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3)
         => k14_ordinal2(c1_10__arytm_3,k1_ordinal1(A)) = k14_ordinal2(k1_ordinal1(A),c1_10__arytm_3) ) ) ),
    introduced(definition,[new_symbol(c1_10_2__arytm_3),file(arytm_3,c1_10_2__arytm_3)]),
    [interesting(0.65),axiom,file(arytm_3,c1_10_2__arytm_3)]).

fof(e1_10_2__arytm_3,assumption,(
    k14_ordinal2(c1_10__arytm_3,c1_10_2__arytm_3) = k14_ordinal2(c1_10_2__arytm_3,c1_10__arytm_3) ),
    introduced(assumption,[file(arytm_3,e1_10_2__arytm_3)]),
    [interesting(0.65),axiom,file(arytm_3,e1_10_2__arytm_3)]).

fof(dt_c1_10_2__arytm_3,assumption,
    ( v3_ordinal1(c1_10_2__arytm_3)
    & v4_ordinal2(c1_10_2__arytm_3) ),
    introduced(assumption,[file(arytm_3,c1_10_2__arytm_3)]),
    [interesting(0.65),axiom,file(arytm_3,c1_10_2__arytm_3)]).

fof(t45_ordinal2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)) ) ) ),
    file(ordinal2,t45_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,t45_ordinal2)]).

fof(e1_10_2_3__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,c1_10__arytm_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__arytm_3,dt_c1_10_2__arytm_3,e1_10_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,fc2_ordinal1,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_xboole_0,rc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_c1_10__arytm_3,dt_c1_10_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc3_ordinal1,e1_10_2__arytm_3,t45_ordinal2]),
    [interesting(0.5),file(arytm_3,e1_10_2_3__arytm_3),[file(arytm_3,e1_10_2_3__arytm_3)]]).

fof(s1_arytm_3__e5_10_2__arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ( k14_ordinal2(k1_ordinal1(A),k1_xboole_0) = k1_ordinal1(k14_ordinal2(A,k1_xboole_0))
          & ! [B] : 
              ( ( v3_ordinal1(B)
                & v4_ordinal2(B) )
             => ( k14_ordinal2(k1_ordinal1(A),B) = k1_ordinal1(k14_ordinal2(A,B))
               => k14_ordinal2(k1_ordinal1(A),k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,k1_ordinal1(B))) ) ) )
       => ! [B] : 
            ( ( v3_ordinal1(B)
              & v4_ordinal2(B) )
           => k14_ordinal2(k1_ordinal1(A),B) = k1_ordinal1(k14_ordinal2(A,B)) ) ) ) ),
    file(arytm_3,s1_arytm_3__e5_10_2__arytm_3),
    [interesting(0.9),axiom,file(arytm_3,s1_arytm_3__e5_10_2__arytm_3)]).

fof(e1_10_2_1__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_xboole_0) = k1_ordinal1(c1_10_2__arytm_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,t2_subset,antisymmetry_r2_hidden,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_k1_xboole_0,dt_c1_10_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc1_xboole_0,fc2_ordinal1,fc3_ordinal1,t6_boole,t44_ordinal2]),
    [interesting(0.5),file(arytm_3,e1_10_2_1__arytm_3),[file(arytm_3,e1_10_2_1__arytm_3)]]).

fof(e2_10_2_1__arytm_3,plain,(
    k1_ordinal1(c1_10_2__arytm_3) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,t2_subset,antisymmetry_r2_hidden,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_k1_xboole_0,dt_c1_10_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc1_xboole_0,fc2_ordinal1,fc3_ordinal1,t6_boole,t44_ordinal2]),
    [interesting(0.5),file(arytm_3,e2_10_2_1__arytm_3),[file(arytm_3,e2_10_2_1__arytm_3)]]).

fof(e2_10_2__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_xboole_0) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_xboole_0)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_10_2__arytm_3])],[e1_10_2_1__arytm_3,e2_10_2_1__arytm_3]),
    [interesting(0.65),file(arytm_3,e2_10_2__arytm_3),[file(arytm_3,e2_10_2__arytm_3)]]).

fof(e3_10_2__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_xboole_0) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_xboole_0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,t2_subset,antisymmetry_r2_hidden,t1_subset,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,fc3_ordinal1,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_k1_xboole_0,dt_c1_10_2__arytm_3,fc1_ordinal1,fc1_xboole_0,fc2_ordinal1,t6_boole,e2_10_2__arytm_3]),
    [interesting(0.65),file(arytm_3,e3_10_2__arytm_3),[file(arytm_3,e3_10_2__arytm_3)]]).

fof(dh_c1_10_2_2__arytm_3,definition,
    ( ( ( v3_ordinal1(c1_10_2_2__arytm_3)
        & v4_ordinal2(c1_10_2_2__arytm_3) )
     => ( k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10_2_2__arytm_3) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,c1_10_2_2__arytm_3))
       => k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ) )
   => ! [A] : 
        ( ( v3_ordinal1(A)
          & v4_ordinal2(A) )
       => ( k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),A) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,A))
         => k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(A)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(A))) ) ) ),
    introduced(definition,[new_symbol(c1_10_2_2__arytm_3),file(arytm_3,c1_10_2_2__arytm_3)]),
    [interesting(0.5),axiom,file(arytm_3,c1_10_2_2__arytm_3)]).

fof(e1_10_2_2__arytm_3,assumption,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10_2_2__arytm_3) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,c1_10_2_2__arytm_3)) ),
    introduced(assumption,[file(arytm_3,e1_10_2_2__arytm_3)]),
    [interesting(0.5),axiom,file(arytm_3,e1_10_2_2__arytm_3)]).

fof(dt_c1_10_2_2__arytm_3,assumption,
    ( v3_ordinal1(c1_10_2_2__arytm_3)
    & v4_ordinal2(c1_10_2_2__arytm_3) ),
    introduced(assumption,[file(arytm_3,c1_10_2_2__arytm_3)]),
    [interesting(0.5),axiom,file(arytm_3,c1_10_2_2__arytm_3)]).

fof(e1_10_2_2_1__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10_2_2__arytm_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,fc2_ordinal1,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_xboole_0,rc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc3_ordinal1,t45_ordinal2]),
    [interesting(0.35),file(arytm_3,e1_10_2_2_1__arytm_3),[file(arytm_3,e1_10_2_2_1__arytm_3)]]).

fof(e2_10_2_2_1__arytm_3,plain,(
    k1_ordinal1(k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,e1_10_2_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,fc2_ordinal1,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_xboole_0,rc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc3_ordinal1,e1_10_2_2__arytm_3,t45_ordinal2]),
    [interesting(0.35),file(arytm_3,e2_10_2_2_1__arytm_3),[file(arytm_3,e2_10_2_2_1__arytm_3)]]).

fof(e2_10_2_2__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,e1_10_2_2__arytm_3])],[e1_10_2_2_1__arytm_3,e2_10_2_2_1__arytm_3]),
    [interesting(0.5),file(arytm_3,e2_10_2_2__arytm_3),[file(arytm_3,e2_10_2_2__arytm_3)]]).

fof(e3_10_2_2__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,e1_10_2_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_ordinal1,fc1_xboole_0,fc2_ordinal1,rc1_arytm_3,rc1_ordinal1,rc3_ordinal1,t1_subset,cc1_ordinal1,cc2_arytm_3,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,fc3_ordinal1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,fc1_ordinal1,e2_10_2_2__arytm_3]),
    [interesting(0.5),file(arytm_3,e3_10_2_2__arytm_3),[file(arytm_3,e3_10_2_2__arytm_3)]]).

fof(i3_10_2_2__arytm_3,theorem,(
    $true ),
    introduced(tautology,[file(arytm_3,i3_10_2_2__arytm_3)]),
    [interesting(0.5),trivial,file(arytm_3,i3_10_2_2__arytm_3)]).

fof(i2_10_2_2__arytm_3,plain,(
    k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3,e1_10_2_2__arytm_3])],[e3_10_2_2__arytm_3,i3_10_2_2__arytm_3]),
    [interesting(0.5),file(arytm_3,i2_10_2_2__arytm_3),[file(arytm_3,i2_10_2_2__arytm_3)]]).

fof(i1_10_2_2__arytm_3,plain,
    ( k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10_2_2__arytm_3) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,c1_10_2_2__arytm_3))
   => k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10_2__arytm_3,dt_c1_10_2_2__arytm_3]),discharge_asm(discharge,[e1_10_2_2__arytm_3])],[e1_10_2_2__arytm_3,i2_10_2_2__arytm_3]),
    [interesting(0.5),file(arytm_3,i1_10_2_2__arytm_3),[file(arytm_3,i1_10_2_2__arytm_3)]]).

fof(i1_10_2_2_tmp__arytm_3,plain,
    ( ( v3_ordinal1(c1_10_2_2__arytm_3)
      & v4_ordinal2(c1_10_2_2__arytm_3) )
   => ( k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10_2_2__arytm_3) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,c1_10_2_2__arytm_3))
     => k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(c1_10_2_2__arytm_3)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(c1_10_2_2__arytm_3))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10_2__arytm_3]),discharge_asm(discharge,[dt_c1_10_2_2__arytm_3])],[dt_c1_10_2_2__arytm_3,i1_10_2_2__arytm_3]),
    [interesting(0.65),e4_10_2__arytm_3]).

fof(e4_10_2__arytm_3,plain,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),A) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,A))
       => k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),k1_ordinal1(A)) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,k1_ordinal1(A))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_10_2__arytm_3])],[i1_10_2_2_tmp__arytm_3,dh_c1_10_2_2__arytm_3]),
    [interesting(0.65),file(arytm_3,e4_10_2__arytm_3),[file(arytm_3,e4_10_2__arytm_3)]]).

fof(e5_10_2__arytm_3,plain,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),A) = k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,A)) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_10_2__arytm_3])],[cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,dt_k14_ordinal2,dt_k1_ordinal1,dt_k1_xboole_0,dt_c1_10_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc1_xboole_0,fc2_arytm_3,fc2_ordinal1,fc3_arytm_3,fc3_ordinal1,s1_arytm_3__e5_10_2__arytm_3,e3_10_2__arytm_3,e4_10_2__arytm_3]),
    [interesting(0.65),file(arytm_3,e5_10_2__arytm_3),[file(arytm_3,e5_10_2__arytm_3)]]).

fof(e2_10_2_3__arytm_3,plain,(
    k1_ordinal1(k14_ordinal2(c1_10_2__arytm_3,c1_10__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__arytm_3,dt_c1_10_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,fc2_ordinal1,t1_subset,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_xboole_0,rc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_c1_10__arytm_3,dt_c1_10_2__arytm_3,cc1_ordinal1,fc1_ordinal1,fc2_arytm_3,fc3_arytm_3,fc3_ordinal1,e5_10_2__arytm_3]),
    [interesting(0.5),file(arytm_3,e2_10_2_3__arytm_3),[file(arytm_3,e2_10_2_3__arytm_3)]]).

fof(e6_10_2__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ),
    inference(iterative_eq,[status(thm),assumptions([e1_10_2__arytm_3,dt_c1_10__arytm_3,dt_c1_10_2__arytm_3])],[e1_10_2_3__arytm_3,e2_10_2_3__arytm_3]),
    [interesting(0.65),file(arytm_3,e6_10_2__arytm_3),[file(arytm_3,e6_10_2__arytm_3)]]).

fof(e7_10_2__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ),
    inference(mizar_by,[status(thm),assumptions([e1_10_2__arytm_3,dt_c1_10__arytm_3,dt_c1_10_2__arytm_3])],[existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_ordinal1,fc1_xboole_0,fc2_ordinal1,rc1_arytm_3,rc1_ordinal1,rc3_ordinal1,t1_subset,cc1_ordinal1,cc2_arytm_3,cc3_ordinal1,fc2_arytm_3,fc3_arytm_3,fc3_ordinal1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,dt_k14_ordinal2,dt_k1_ordinal1,dt_c1_10__arytm_3,dt_c1_10_2__arytm_3,fc1_ordinal1,e6_10_2__arytm_3]),
    [interesting(0.65),file(arytm_3,e7_10_2__arytm_3),[file(arytm_3,e7_10_2__arytm_3)]]).

fof(i3_10_2__arytm_3,theorem,(
    $true ),
    introduced(tautology,[file(arytm_3,i3_10_2__arytm_3)]),
    [interesting(0.65),trivial,file(arytm_3,i3_10_2__arytm_3)]).

fof(i2_10_2__arytm_3,plain,(
    k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ),
    inference(conclusion,[status(thm),assumptions([e1_10_2__arytm_3,dt_c1_10__arytm_3,dt_c1_10_2__arytm_3])],[e7_10_2__arytm_3,i3_10_2__arytm_3]),
    [interesting(0.65),file(arytm_3,i2_10_2__arytm_3),[file(arytm_3,i2_10_2__arytm_3)]]).

fof(i1_10_2__arytm_3,plain,
    ( k14_ordinal2(c1_10__arytm_3,c1_10_2__arytm_3) = k14_ordinal2(c1_10_2__arytm_3,c1_10__arytm_3)
   => k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__arytm_3,dt_c1_10_2__arytm_3]),discharge_asm(discharge,[e1_10_2__arytm_3])],[e1_10_2__arytm_3,i2_10_2__arytm_3]),
    [interesting(0.65),file(arytm_3,i1_10_2__arytm_3),[file(arytm_3,i1_10_2__arytm_3)]]).

fof(i1_10_2_tmp__arytm_3,plain,
    ( ( v3_ordinal1(c1_10_2__arytm_3)
      & v4_ordinal2(c1_10_2__arytm_3) )
   => ( k14_ordinal2(c1_10__arytm_3,c1_10_2__arytm_3) = k14_ordinal2(c1_10_2__arytm_3,c1_10__arytm_3)
     => k14_ordinal2(c1_10__arytm_3,k1_ordinal1(c1_10_2__arytm_3)) = k14_ordinal2(k1_ordinal1(c1_10_2__arytm_3),c1_10__arytm_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__arytm_3]),discharge_asm(discharge,[dt_c1_10_2__arytm_3])],[dt_c1_10_2__arytm_3,i1_10_2__arytm_3]),
    [interesting(0.8),e3_10__arytm_3]).

fof(e3_10__arytm_3,plain,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3)
       => k14_ordinal2(c1_10__arytm_3,k1_ordinal1(A)) = k14_ordinal2(k1_ordinal1(A),c1_10__arytm_3) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_10__arytm_3])],[i1_10_2_tmp__arytm_3,dh_c1_10_2__arytm_3]),
    [interesting(0.8),file(arytm_3,e3_10__arytm_3),[file(arytm_3,e3_10__arytm_3)]]).

fof(e4_10__arytm_3,plain,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_10__arytm_3])],[cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,dt_k14_ordinal2,dt_k1_ordinal1,dt_k1_xboole_0,dt_c1_10__arytm_3,cc1_ordinal1,fc1_ordinal1,fc1_xboole_0,fc2_arytm_3,fc2_ordinal1,fc3_arytm_3,fc3_ordinal1,s1_arytm_3__e4_10__arytm_3,e2_10__arytm_3,e3_10__arytm_3]),
    [interesting(0.8),file(arytm_3,e4_10__arytm_3),[file(arytm_3,e4_10__arytm_3)]]).

fof(e5_10__arytm_3,plain,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__arytm_3])],[cc2_ordinal1,rc1_ordinal1,dt_k14_ordinal2,dt_c1_10__arytm_3,cc1_ordinal1,fc3_arytm_3,e4_10__arytm_3]),
    [interesting(0.8),file(arytm_3,e5_10__arytm_3),[file(arytm_3,e5_10__arytm_3)]]).

fof(i2_10__arytm_3,theorem,(
    $true ),
    introduced(tautology,[file(arytm_3,i2_10__arytm_3)]),
    [interesting(0.8),trivial,file(arytm_3,i2_10__arytm_3)]).

fof(i1_10__arytm_3,plain,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_10__arytm_3])],[e5_10__arytm_3,i2_10__arytm_3]),
    [interesting(0.8),file(arytm_3,i1_10__arytm_3),[file(arytm_3,i1_10__arytm_3)]]).

fof(i1_10_tmp__arytm_3,plain,
    ( ( v3_ordinal1(c1_10__arytm_3)
      & v4_ordinal2(c1_10__arytm_3) )
   => ! [A] : 
        ( ( v3_ordinal1(A)
          & v4_ordinal2(A) )
       => k14_ordinal2(c1_10__arytm_3,A) = k14_ordinal2(A,c1_10__arytm_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_10__arytm_3])],[dt_c1_10__arytm_3,i1_10__arytm_3]),
    [interesting(1),t3_arytm_3]).

fof(t3_arytm_3,theorem,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => k14_ordinal2(A,B) = k14_ordinal2(B,A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_10_tmp__arytm_3,dh_c1_10__arytm_3]),
    [interesting(1),file(arytm_3,t3_arytm_3),[file(arytm_3,t3_arytm_3)]]).