% Mizar problem: t12_wellord2,wellord2,251,9 
fof(t12_wellord2,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r4_wellord1(A,k1_wellord2(B))
                  & r4_wellord1(A,k1_wellord2(C)) )
               => B = C ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_ordinal1,cc2_ordinal1,dt_k1_wellord2,rc1_ordinal1,t11_wellord2,t50_wellord1,t52_wellord1]),
    [file(wellord2,t12_wellord2)]).

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

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

fof(dt_k1_wellord2,axiom,(
    ! [A] : v1_relat_1(k1_wellord2(A)) ),
    file(wellord2,k1_wellord2),
    []).

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

fof(t11_wellord2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r4_wellord1(k1_wellord2(A),k1_wellord2(B))
           => A = B ) ) ) ),
    file(wellord2,t11_wellord2),
    []).

fof(t50_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
           => r4_wellord1(B,A) ) ) ) ),
    file(wellord1,t50_wellord1),
    []).

fof(t52_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => ( ( r4_wellord1(A,B)
                  & r4_wellord1(B,C) )
               => r4_wellord1(A,C) ) ) ) ) ),
    file(wellord1,t52_wellord1),
    []).