% Mizar problem: t3_arytm_3,arytm_3,148,47 
fof(t3_arytm_3,conjecture,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & v4_ordinal2(B) )
         => k14_ordinal2(A,B) = k14_ordinal2(B,A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,dt_k14_ordinal2,dt_k1_ordinal1,dt_k1_xboole_0,dt_m1_subset_1,existence_m1_subset_1,fc1_ordinal1,fc1_xboole_0,fc2_arytm_3,fc2_ordinal1,fc3_arytm_3,fc3_ordinal1,rc1_arytm_3,rc1_ordinal1,rc1_xboole_0,rc2_ordinal1,rc2_xboole_0,rc3_ordinal1,s1_arytm_3__e4_10__arytm_3,s1_arytm_3__e5_10_2__arytm_3,t1_subset,t2_subset,t44_ordinal2,t45_ordinal2,t47_ordinal2,t6_boole,t7_boole,t8_boole]),
    [file(arytm_3,t3_arytm_3)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_arytm_3,axiom,(
    ! [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),
    []).

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

fof(cc2_arytm_3,axiom,(
    ! [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),
    []).

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

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

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

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

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_arytm_3,axiom,(
    ! [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),
    []).

fof(fc2_ordinal1,axiom,
    ( 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),
    []).

fof(fc3_arytm_3,axiom,(
    ! [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),
    []).

fof(fc3_ordinal1,axiom,(
    ! [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),
    []).

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

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

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_ordinal1,axiom,(
    ? [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),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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

fof(s1_arytm_3__e4_10__arytm_3,axiom,(
    ! [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),
    []).

fof(s1_arytm_3__e5_10_2__arytm_3,axiom,(
    ! [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),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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

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

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

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).